TA 


Technical   Drawing  Series 


lOO 


UC-NRLF 


TOPOGRAPHICAL  DRAWING 


DANIELS 


TECHNICAL    DRAWING    SERIES 


A  TEXT-BOOK 

OF 


TOPOGRAPHICAL    DRAWING 


BY 

FRANK   T.    DANIELS,  A.M.B. 

AUTHOR    OF    "  A    TEXT-BOOK    OF    FREE-HAND    LETTERING ' 


BOSTON,   U.S.A. 
D.    C.    HEATH   &   CO.,   PUBLISHERS 

1908 


COPYRIGHT,  1907, 
BY  FRANK  T.   DANIELS. 


PREFACE 

THIS  book  is  offered  to  supply  the  need  which  several  years'  experience  in  giving  instruc- 
tion to  students  of  engineering  led  the  author  to  perceive. 

It  presents  the  technical  details  of  topographical  drawing,  together  with  problems 
involving  the  design  of  earthwork  structures,  and  calculations  relating  to  them. 

A  leading  feature  of  the  other  books  of  the  "  Technical  Drawing  Series  "  has  been  fol- 
lowed ;  namely,  the  presentation  of  exercises  and  problems  each  with  a  definite  lay-out,  thus 
adapting  the  book  for  use  in  large  classes. 

It  is  assumed  that  the  student  will  have  acquired  some  proficiency  in  mechanical  drawing 
before  taking  up  the  work  here  presented,  therefore  the  descriptions  of  instruments  and 
explanations  of  processes  do  not  include  those  which  are  ordinarily  given  in  a  good  course 
in  mechanical  drawing.  Indeed,  the  aim  throughout  the  preparation  of  the  book  has  been 
to  avoid  duplicating  anything  that  the  student  may  well  learn  from  some  other  source ;  also 
to  gather  into  form  immediately  available  to  a  draftsman  those  things  which  his  other  books 
cannot  consistently  include,  or  which  are  not  presented  in  a  sufficiently  concrete  form  to  be 
of  the  greatest  use. 

BOSTON,  MASSACHUSETTS,  _-  O  O  U  O  G 

December,  1906. 

iii 


TABLE   OF  CONTENTS 


1.  Definition 

2.  Implements  and  Materials 

3.  Beam  Compasses 

4.  The  Contour  or  Curve  Pen 

5.  The  Railroad  Pen 

6.  Proportional  Dividers 

7.  Scales        . 

8.  Curves       .... 

9.  Protractors 

10.  Section  Liner    . 

11.  The  Planimeter 

12.  The  Pantograph 


CHAPTER  I 

INTRODUCTORY 

PAGE          ART. 

1 
1 

2 

13. 
14. 

15. 

The  Copying  Glass  . 
The  Straightedge 
Needle  Point  or  Pricker 

3 
3 
3 

16. 
17. 

18. 

Paper  Weights 
Paper 
Pens  and  Holder 

• 

4 

19. 

Brushes     . 

. 

6 

20. 

WTater  Glass 

6 

21. 

Color  Saucers    . 

. 

8 

22. 

Colors 

9 

23. 

Colored  Pencils 

.      10 

PAGE 
11 

12 

12 
13 
13 

16 
17 
17 
17 
18 
18 


CHAPTER   II 
PRELIMINARY  PROBLEMS   AND  OPERATIONS 


24.  To  divide  a  Given  Distance  into  Equal  Parts  19 

25.  To  divide  an  Arc  into  Equal  Parts  ...  19 

26.  To  find  Points  on  an  Arc  of  Large  Radius       .  20 

27.  Multipliers  for  Planimeter  Measurements        .  21 

28.  Rating  the  Planimeter 21 


29.  Stretching  Paper 

30.  Mounting  Paper  on  Cloth 

31.  Splicing  Paper 

32.  Patching  Tracing  Cloth  . 


23 

25 
26 
27 


VI 


TABLE   OF  CONTENTS 


33.  The  General  Problem       . 

34.  Plotting  a  Triangulation 

35.  Plotting  Progressive  Angles     . 

36.  Protracting  an  Angle 

37.  To  plot  an  Angle  by  its  Tangent 

38.  To  plot  an  Angle  by  the  Chord  of  its  Sub- 

tended Arc  .... 

39.  Defect  of  Plotting  Progressive  Angles 


CHAPTER 

Ill 

PLOTTING 

PAGE          ART. 

PAGE 

.      28 

40. 

Deflection  Angle 

31 

.      28 

41. 

Bearings  . 

.... 

32 

.      29 

42. 

Azimuth    . 

33 

.      29 

43. 

Plotting  by  Total  Latitudes  and  Longitudes 

33 

.      30 

44. 

Surveys  based  on 

a  System  of  Coordinates 

35 

ib- 

45. 

Plotting  Surface 

Markings       .         .         . 

37 

.      30 

46. 

Problems  . 

..... 

39 

.      30 

CHAPTER   IV 
TOPOGRAPHICAL   DRAWING  IN  INK 


47.  Topographical  Symbols  in  General 

48.  The  Sizes  and  Distribution  of  Symbols 

49.  Grass  Land       .... 

50.  Cleared  Land    .... 

51.  Cultivated  Land 

52.  Sand,  Gravel,  and  Mud    . 

53.  Trees 

54.  Foliage  in  Mass 

55.  Fresh  Marsh 


42 
43 
44 
45 
45 
46 
47 
47 
48 


56.  Salt  Marsh 

57.  Water 

58.  Roads  and  Streets    . 

59.  Railways  . 

60.  Embankments  and  Cuts 

61.  Ledge 

62.  Fence,  Wall,  and  Hedge 

63.  Buildings  . 

64.  Exercises  . 


49 
49 
51 
51 
51 
52 
52 
52 
57 


CHAPTER  V 
TOPOGRAPHICAL  DRAWING  IN  COLORS 


65.  Preparation  of  the  Color 

66.  The  Nature  of  a  Tint 

67.  Applying  the  Color 


58 
58 
59 


68.  Inking 

69.  Making  Corrections 

70.  Laying  a  Graded  Tint 


61 
62 
62 


TABLE   OF   CONTENTS 


vn 


ART. 

71.  Blending          .... 

72.  Mottling          .... 

73.  Dragging         .... 

74.  Matching  a  Color   . 

75.  Combinations  of  Colors  . 

76.  Special  Combinations  of  Colors 

77.  Topographical  Drawing  in  Colors 

78.  Grass  Land 

79.  Cleared  Land  . 

80.  Cultivated  Land 

81.  Sand  and  Gravel 

82.  Mud 

83.  Individual  Trees 

84.  Trees  in  Mass 

85.  Fresh  Marsh    . 

86.  Salt  Marsh      . 

87.  Water     . 

88.  Streets  and  Roads 

89.  Railways 


PAGE 

ART. 

63 

90. 

64 

91. 

65 

92. 

66 

93. 

67 

94. 

68 

95. 

69 

96. 

70 

70 

97. 

70 

98. 

70 

99. 

70 

70 

100. 

73 

101. 

.  73 

102. 

74 

103. 

74 

77 

104. 

77 

PAGE 

Embankments  and  Cuts         ....  77 

Ledge,  or  Rocky  Surface         ....  77 

Fences,  Walls,  and  Hedges    ....  77 

Buildings 78 

Use  of  Colored  Pencils 78 

Use  of  the  Stump 79 

Colored    Pencils   with    Tracing    Paper   and 

Tracing  Cloth 79 

Colors  in  relation  to  Blueprinting          .         .  80 

Colored  Whiteprints 80 

Exercises  in  Water  Coloring ;  General  Direc- 
tions    80 

Exercise  in  Flat  Tints 81 

Exercise  in  Graded  Tints  and  in  Mottling     .  81 

Exercise  in  Conventional  Tints  and  Symbols  81 
Exercise  in  Conventional  Tints  and  Symbols 

(continued)         ......  82 

Application  of  Conventional  Tints  and  Sym- 
bols  .  83 


CHAPTER  VI 
SURFACE   FORMS  AND  EARTHWORK 


105.  Representation  of  Surface  Forms  ...  84 

106.  Representation  by  Recorded  Elevations          .  85 

107.  Representation  by  Profile       ....  85 

108.  Cross-sections 87 

109.  Representation  by  Contour  Lines  ...  87 

110.  Interpolation  of  Contours       .         .         .         .89 

111.  Interpolation  from  Corners  of  Rectangles      .  90 

112.  Interpolation  on  the  Assumption  of  Straight 

Grades 92 


113.  Summary  of  Principles  regarding  Contours  93 

114.  Determination   of   Slopes    and    their   Inter- 

sections        94 

115.  Earthwork,  General  Statement       ...  97 

116.  Method  by  Four-sided  Prisms        ...  97 

117.  Method  by  Three-sided  Prisms       ...  98 

118.  The  Prismoidal  Method          ....  99 

119.  Consecutive  Prismoids 100 

120.  Application  of  Prismoidal  Method  to  Grading  101 


Vlll 


TABLE  OF  CONTENTS 


AET.  PAGE 

121.  Methods     approximating     the     Prismoidal 

Method 101 

122.  Volume  from  a  Contour  Map         .        .        .  102 


123.  Treatment  of  the  Plan   . 

124.  Balancing  Cuts  and  Fills 

125.  Problems 


PAGE 

106 
107 
108 


CHAPTER  VII 
CONVENTIONAL  TREATMENT  FOR   SURFACES  AND   SECTIONS 


126.  Reasons  for  Treatment  .        . 

127.  Materials  in  Elevation    . 

128.  Materials  in  Section 

129.  Materials  in  Section  (continued) 


115 
115 
120 
124 


130.   Geological  Profiles  and  Sections     .        .        .128 

181.   Borings 133 

132.   Illustration  of  Cross-sectioning  and  Render- 
ing      •     .        .        .        .133 


CHAPTER  VIII 
COPYING,   REDUCTION,    AND  ENLARGEMENT  OF  PLANS 


133.  Copying  by  Blueprinting 

134.  The  Sensitizing  Solution 

135.  Making  Corrections  on  Blueprints 

136.  The  Printing  Value  of  Colors 

137.  Printing  from  a  Thick  Drawing     . 

138.  Copying  by  Means  of  Vandyke  Negatives 

139.  Making  Corrections  on  Vandyke  Negatives 

140.  Special  Uses  of  Vandyke  Negatives 

141.  Use  of  the  Copying  Glass 


134 
135 
136 
136 
137 
137 
138 
138 
139 


142.  Copying  by  Pricking 

143.  Copying  with  Transfer  Paper 

144.  Copying,    Enlarging,  and  Reducing  by  the 

Pantograph 

145.  Reducing   and    Enlarging   by    Proportional 

Squares      .         .         .         .         .         •  .      • 

146.  Photography,    Lithography,    and    Photo-en- 

graving     ....... 

147.  Color  Work  by  Photo-engraved  Plates  . 


139 
139 

140 
140 

142 
143 


A    TEXT-BOOK    OF 
TOPOGRAPHICAL    DRAWING 


TEXT-BOOK  OF  TOPOGRAPHICAL  DRAWING 


CHAPTER   I 

INTRODUCTORY 

1.  Definition.     Topographical    Drawing    is    the    art    of    representing    in    a   graphical 
manner,  a    limited  portion  of   the    earth's   surface,  including  not  only  the   natural  features, 
such  as  trees,  streams,  and  marshes,  but  also  such  artificial  features  as  roads  and  buildings. 

These  objects  are  shown  in  their  true  geographical  relations,  and,  although  the  represen- 
tation is  made  on  a  single  flat  sheet  of  paper,  the  surface  configuration  is  generally  indicated. 
Sometimes  this  is  done  in  a  relative  way  only,  showing  where  elevations  and  depressions 
occur,  and  sometimes  sufficient  information  is  given  so  that  the  exact  heights  and  depths 
can  be  determined  from  the  drawing. 

The  geographical  positions  of  objects  are  fixed  in  accordance  with  some  suitable  pre- 
determined scale,  so  that  the  drawing  is  an  exact  representation  of  the  portion  of  the 
earth's  surface  shown,  including  the  artificial  features  referred  to.  Horizontal  distances 
can  therefore  be  measured  on  the  finished  drawing  by  using  the  scale  that  was  employed 
in  making  it. 

2.  Implements   and  Materials.     It   is   assumed   that   the   student   is   familiar   with   the 
instruments,  materials,  and  operations    of   ordinary  mechanical  drawing.     Hence   only  such 
of  these  as  are  used  particularly  in  topographical  drawing  will  be  described. 

1 


INSTRUMENTS  AND   THEIR   USE 


3.  Beam  Compasses.  This  instrument  is  used  for  drawing  arcs  of  greater  radius  than 
is  possible  with  the  ordinary  compasses  and  extension  bar,  and  even  for  arcs  which  are 
within  the  range  of  the  latter,  when  very  exact  work  is  necessary. 

The  instrument  consists  of  two  blocks  of  German  silver,  Fig.  1,  each  having  a  socket  at 
its  lower  edge.  Into  one  of  these  can  be  fitted  a  leg  carrying  a  needle  point  for  the  center. 
The  leg  in  the  other  block  carries  either  a  pen  or  pencil  point.  The  blocks  are  fastened  to  a 
long  "  beam  "  of  hard  wood  by  means  of  the  screws  A,  A.  The  leg  carrying  the  needle  point 
is  pivoted  at  B,  and  its  motion  around  the  pivot  is  controlled  by  the  spring  S,  and  the  thumb 
nut  N.  The  required  radius  is  first  obtained  approximately  by  sliding  the  blocks  along  the 
beam.  After  having  clamped  them,  the  adjustment  to  the  exact  radius  is  secured  by  turning 
the  nut.  There  is  shown  also  an  end  view  of  a  block  and  the  beam.  It  will  be  noted  that  the 

screws  A,  A  do  not  bear  directly 
upon  the  beam,  but  upon  interme- 
diate strips  of  metal.  These  strips 
do  not  extend  to  the  bottom  of  the 
slots  in  the  blocks,  and  the  spaces 
thus  left  are  occupied  by  a  slight 
projection  on  the  lower  edge  of  the 
beam,  the  purpose  of  which  is  to 
prevent  the  blocks  from  dropping 
off  when  the  thumb  nut  is  loosened. 
It  is  convenient  to  have  three  or  four  beams 
Fig.  1 .  V  varying  from  one  to  six  or  eight  feet  in  length. 


N 


PENS 


4.  The  Contour  or  Curve  Pen.    This  is  like  a  right-line  pen  except  that  the  blades  are  curved, 
as  shown  in  Fig.  2,  and  the  shank  passes  entirely  through  the  handle,  terminating  in  a  nut  at 
the  top.      When  this  nut  is  loose,  the  pen 

swivels  freely  in  the  handle.     The  purpose 

of  the   pen  is   for  drawing   free-hand  lines, 

such  as  contour  lines  (Art.  109).     In  use  the 

instrument  is  held  vertically.     Because  of  their  curved  form  the  blades  trail  along  after  the 

handle,  thus  causing  them  to  be  always  in  a  position  to  yield  a  line  of  uniform  thickness.     To 

obtain  the  same  result  with  the  right-line  pen  a  constant  turning  of  the  wrist  is  necessary. 

5.  The  Railroad  Pen.     This,  as  shown  in  Fig.  3,  is  simply  a  double-pointed,  right-line  pen. 
Its  use  saves  much  time  when  many  parallel  lines  are  to  be  drawn,  as  those  showing  the  rails 

of  a  railroad  track,  or  the  side  lines  of 
I     roads.    It  is  also  useful  for  drawing  very 
wide  lines.     For  this  purpose  the  points 
£'  are  brought  near  together,  the  blades  in 

each  point  are  opened  wide,  and  ink  is  placed  not  only  between  the  blades,  but  also  between 
the  points.     With  the  proper  adjustment  of  distances  between  points  and  blades  a  line  fully 
one  eighth   of   an  inch  wide  can  be  drawn 
with  fairly  square  ends. 

6.  Proportional  Dividers.     As  shown  by 
Fig.  4  this  form  of  dividers  has  points  at 

each  end.     The  pivot  can  be  shifted  along  Fig.  4. 


4  INSTRUMENTS  AND  THEIR   USE 

the  slots  in  the  legs  so  that  any  desired  ratio  of  opening  between  the  points  at  the  opposite 
ends  of  the  instrument  can  be  secured. 

The  principal  use  of  this  instrument  is  in  reducing  and  enlarging  maps,  Sect.  145. 

7.  Scales.  A  map  is  necessarily  very  much  smaller  than  the  portion  of  the  earth's  surface 
which  it  represents,  and  the  scales  used  for  architectural  and  mechanical  drawing  are,  therefore, 
not  suitable  for  topographical  drawing. 

The  scales  generally  used  in  topography  are  called  "  scales  of  equal  parts,"  or  "  chain 
scales."  For  instance,  a  scale  of  1  inch  =  40  feet,  means  that  an  inch  on  the  scale  is  taken  to 
represent  forty  feet  on  the  ground.  The  inch  is  then  divided  into  forty  equal  parts,  each  of 
which  represents  one  foot  on  the  ground.  But  since  the  lines  to  be  drawn  may  repre- 
sent many  times  forty  feet,  the  whole  edge  of  the  scale  (from  one  to  two  feet  long)  is 
divided  into  fortieths  of  an  inch,  and  each  twentieth  division  is  numbered.  Thus  the  scale 
above  described  (often  called  simply  "a  forty  scale")  if  made  twelve  inches  long  will  con- 
tain 480  divisions,  the  last  one  being  numbered  simply  48,  the  final  0  being  understood  at 
each  numbered  division.  A  drawing  made  to  this  scale  will  bear  a  ratio  in  its  linear  di- 

mensions of   r-^  -  jTr  =  jTT-r  to  the  lines  upon  the  ground  which  it  represents. 


The  scales  usually  employed  in  topographical  drawing  have  the  inch  divided  into  10,  20, 
30,  40,  50,  60,  80,  and  100  parts.  Drawings  are  often  made  to  a  scale  of  1  in.  =  300  ft., 
but  the  scale  used  is  the  "  thirty  scale,"  the  intervals  on  the  scale  being  mentally  multiplied 
by  ten. 

Scales  are  made  of  Bristol  board,  boxwood,  and  steel.     The  first  are  not  accurate  enough 


for  fine  work.     Those  made  of  boxwood  are  most  satisfactory,  especially  if  the  edges  are 
finished  with  strips  of  white  celluloid  on  which  the  divisions  are  marked  in  black. 

Fig.  5  shows  the  triangular  and  flat  forms  of  boxwood  scales.     The  former  contains  six 
scales,  the  latter  contains  two. 

The  chief  objection  to  the  triangular  form  is  that  it  must  rest  on  the  divided  edges  and 
the  divisions  get  worn  away.  Another  objection  is  that  the  wrong  scale  is  more  liable  to 
be  used  than  is  the  case  with  the  flat  form. 
For  instance  the  30  and  40  scales  of  the 
triangular  form  may  easily  be  mistaken  for 
one  another,  while  the  two  scales  on  the 
flat  form  are  very  different,  such  as  10  and 
40,  so  that  they  are  not  as  liable  to  be  con- 
founded. 

This  last  objection  to  the  triangular 
form  may  be  overcome  by  the  use  of  a 
"  scale  guard."  This  is  a  metal  clip  which 
is  placed  on  the  top  angle  of  the  scale. 


(if 1 1  if  1 1  if  1 1  if  1 1  if 


Fig.  5. 


It   should  be    placed  at   one   end,  as   the 

right,  then  the  draftsman  knows  that  when 

it  is  in  this  position  before  him,  the  proper  scale  for  use  is  at  the  edge  remote  from  the 

body. 

Scale  guards  made  for  this  purpose  alone  are  sold  by  dealers,  but  the  form  of  paper  clip 
shown  in  Fig.  5  is  quite  as  satisfactory  and  much  cheaper. 


INSTRUMENTS  AND  THEIR  USE 


8.  Curves.  Beside  the  "French,"  or  "irregular,"  curves  which  form  a  part  of 
every  draftsman's  outfit,  a  few  ship  curves  and  a  set  of  railroad  curves  are  usually 
found  in  a  drafting  office. 

Ship  Curves  are  made  of  pearwood,  hard  rubber,  or  celluloid.  Fig.  6  shows  a 
typical  form.  They  are  about  24  inches  long,  and  contain  long, 
sweeping  curves  of  constantly  varying  radius. 

Railroad  Curves,  Fig.  7,  are  made  of  cardboard,  pearwood,  hard 
rubber,  celluloid,  or  zinc.  A  set  contains  from  10  to  100  pieces.  The 
set  suitable  for  most  purposes  contains  44  pieces,  which  vary  in  radius 
from  3  to  200  inches,  and  in  length  from  about  5  to  18  inches.  Both 
curved  edges  of  a  piece  are  cut  to  the  same  radius,  and  each  piece  is 
stamped  with  a  number  expressing  its  radius  in  inches. 


9.  Protractors.  The  protractor  is  an  instrument  for  laying  off 
angles  or  for  measuring  angles  already  laid  down  on  the  drawing. 
Protractors  are  made  of  cardboard,  horn,  brass,  German  silver,  steel, 
hard  rubber,  and  celluloid. 

The  simplest  form,  shown  in  Fig.  8,  consists  of  a  semicircular 
sheet.  The  straight  edge  is  parallel  to  the  diameter  of  the  arc,  and 
the  center  is  plainly  marked  by  a  line.  The  edge  is  divided  to  degrees 
which  are  numbered  in  both  directions.  Protractors  of  this  type 

vary  in  diameter  from  about  5  inches  to  14  inches,  the  larger  ones  being  divided  to  |  degrees. 

Cardboard  protractors  are  usually  rectangular  in  form  when  bought.     It  is  best  to  cut  around 


Fig.  6. 


Fig.  7. 


PKOTRACTOKS 


the  curved  portion,  but  to  leave  the  edge 
parallel  to  the  diameter  and  cut  a  notch  to 
the  center  as  shown  in  the  figure.  The 
center  and  ends  of  the  diameter  will  then 
be  protected  from  wear.  When  harder 
material  is  used,  the  instruments  are  made 
to  the  outline  of  the  arc  and  diameter. 

A  type  of  the  more  accurate  form  of 
protractor  is  shown  in  Fig.  9.  German 
silver  is  the  material  commonly  used. 
The  arm  A  is  pivoted  at  the  center  of  the 
arc,  and  a  thin  disk  of  horn  with  two  cross 
lines  ruled  upon  it  accurately  marks  this 
center.  The  beveled  edge  of  the  arm  is 
accurately  radial.  The  arc  or  "limb"  is 
divided  to  ^  degrees,  and  a  vernier  V"  is  en- 
graved on  the  arm,  by  the  use  of  which  the 
latter  can  be  set  to  read  to  single  minutes 
of  the  arc.  This  form  is  called  a  vernier 
protractor,  and  is  made  also  with  a  full 
circle. 

For  methods  of  protracting  angles  see 
Art.  36. 


Fig.  8. 


Fig.  9. 


8 


INSTRUMENTS   AND  THEIR   USE 


10.  Section  Liner.  This  instrument  may  be  classed  as  a  luxury,  but  it  is  very  con- 
venient, especially  in  finishing  the  cross  sections  of  structures.  It  is  simply  for  drawing  parallel, 
equidistant  lines.  Of  course  a  draftsman  should  be  able  to  do  this  well  with  only  a  pair  of 
triangles  and  a  ruling  pen,  without  first  laying  off  the  equidistances.  But  having  acquired  the 

ability  to  do  this  he  may  consider  legitimate  the 
use  of  a  section  liner.  Of  the  many  forms  of 
this  instrument  on  the  market  the  Both  Sec- 
tion Liner  is  satisfactory  and  is  probably  best 
known.  This  is  shown  in  Fig.  10.  The  base 


Fig.  10. 


B  is  a  bar  about  15  inches  long  with  a  rack  R 
fastened  to  it  and  extending  to  within  about  3 
inches  of  the  ends.  In  use  this  base  is  held  down  firmly  by  weights  placed  on  the  ends.  When 
the  knob  K  is  pressed  down,  the  pawl  P,  which  engages  the  teeth  of  the  rack,  causes  the  car- 
riage C  to  move  forward  to  the  right.  Attached  to  the  rear  of  the  carriage  are  the  arc  A  and 
the  ruler  E.  When  the  pressure  on  the  knob  is  released,  a  spiral  spring  throws  it  up  against  the 
check  nut  N,  the  pawl  is  drawn  forward  one  or  more  notches  of  the  rack,  and  all  is  ready  for  a 
repetition  of  the  forward  motion  of  the  carriage  and  its  attachments.  The  teeth  in  the  rack 
are  ^  inch  apart,  and  the  number  of  them  passed  over  by  the  pawl  at  each  pressure  on  the 
knob  depends  upon  the  amount  of  vertical  travel  allowed  in  the  latter  by  the  position  of  N. 

If  the  pawl  passes  over  one  notch  at  each  operation,  the  carriage,  and  consequently  the  ruler, 
will  move  forward  ^  inch,  and  corresponding  multiples  of  this  distance  for  greater  num- 
bers of  notches.  At  each  successive  position  of  the  ruler  a  line  is  drawn  along  its  edge  with 
an  ordinary  ruling  pen. 


THE  PLANIMETEK  9 

When  the  ruler  is  set  at  90°  with  the  base,  it  is  evident  that  the  successive  parallel  posi- 
tions of  its  edge  will  be  distant  from  one  another  an  amount  equal  to  the  successive  movements 
of  the  carriage,  that  is,  ^  inch  for  each  notch  passed  over.  If,  however,  the  ruler  is  set  at  a 
smaller  angle  with  the  base,  the  perpendicular  distances  between  the  ruled  lines  will  be  less 
than  ^j  inch.  If  the  angle  is  30°,  the  lines  will  be  equidistant  ^  x  sin  30°  =  -^  x  ^  =  •£$  inch. 
Usually  the  converse  of  this  operation  is  required,  namely,  to  find  the  setting  of  the  ruler  on 
the  arc  for  a  desired  distance  between  the  ruled  lines.  To  solve  this  case  find  the  natural  sine 
of  the  required  angle  by  dividing  24  (the  number  of  teeth  per  inch  on  the  rack)  by  the  re- 
quired number  of  lines  per  inch.  Thus  for  50  lines  per  inch,  24  -4-  50  =  0.48,  which  is  the 
natural  sine  of  28°  — 41',  the  required  angle.  If  fewer  than  24  lines  per  inch  are  required, 
the  pawl  must  be  set  to  pass  more  than  one  notch,  and  the  proper  substitute  made  for  24 
in  the  above  equations. 

11.     The  Planimeter.     This  is   an  instrument  for  measuring  areas,  and   is  particularly 
useful  in  engineering  work  because  the  areas  of  irregular  figures  are  found  as  easily 
and  accurately  as  those  of  regular  figures. 
The   drawing   from   which  the   measure- 
ment is  made  must  of  course  be  accurately 
drawn  to  scale. 

The  instrument   consists  in  its  sim- 

Fl<y.    |  |  m 

plest  form,  Fig.  11,  of  an  anchor  arm  A  of 

fixed  length,  a  graduated  arm  G  which  slides  in  a  sleeve  S,  and  a  graduated  wheel  W 

carried  on  an  axle  fixed  to  the  framework,  of  which  the  sleeve  is  a  part.     The  anchor 


10 


INSTRUMENTS  AND  THEIR  USE 


point  P  is  thrust  into  the  drawing  and  the  whole  instrument  rotates  about  it.     The  only  other 

points  in  contact  with  the  paper  are  W  and  the  tracing  point  T. 

The  usual  and  most  simple  method  of  using  the  planimeter  is  to  place  P  outside  the 

boundary  of  the  area  to  be  measured.*     T  is  then  moved  carefully  right-handed  around  the 

boundary.  W  rolls  on  the  drawing,  and  the  total  amount 
of  its  rotation  is  read  at  the  vernier.  As  usually  adjusted 
y1^  rotation  of  W  represents  one  square  inch  of  area  on  the 
drawing.  (See  also  Arts.  27  and  28.) 


12.  The  Pantograph.  This  instrument  is  for  copying 
drawings  either  to  the  same,  a  reduced,  or  an  increased 
size.  Its  essential  parts  are  shown  in  Fig.  12.  The  neces- 
sary conditions  are  that  the  four  bars  shall,  by  their  inter- 
sections, form  a  parallelogram,  and  that  F,  T,  and  C  shall 
be  in  a  straight  line.  The  instrument  moves  about  the  fixed 
point  F.  T  is  a  tracing  point  which  is  moved  along  the 
lines  of  the  figure  to  be  copied,  and  C  is  a  pencil  point 
The  ratio  of  linear  dimensions  in  the  copied  and  original  figures 


Fig.  12. 

which  does  the  copying. 


depends  upon  the  manner  in  which  the  bars  are  put  together  to  form  the  parallelogram,  and 

PR      FR 

may  be  expressed  thus:  -^—  =  ^=r=  the  scale  of  enlargement.     If  a  reduction  is  required,  the 


*  For  the  method  of  measuring  large  areas  with  the  anchor  point  inside  the  boundary  see  Eaymond's  "  Plane 
Surveying"  or  Johnson's  "Theory  and  Practice  of  Surveying." 


THE  COPYING   GLASS 


tracing  and  copying  points  must  be  exchanged  ;  if  a  copy  to  the  same  scale  is  required,  the 

arms  must  be  arranged  so  that  — — -  =  2,  and  T  must  become  the  fixed  point. 

OL) 


The  cheap  pantographs  are  made  of  wood,  and 
expensive  instruments  are  made  of  brass  or  steel, 
and  have  many  devices  to  secure  accuracy  and 
convenience  of  operation. 


13.  The  Copying  Glass.  A  panel  of  glass, 
suitably  mounted,  and  illuminated  from  below,  is 
found  most  useful  in  the  drafting  room.  An  ex- 
cellent form  of  such  a  "  copying  glass  "  is  shown 
in  Fig.  13.  The  panel  is  of  plate  glass,  about 
2x3  feet  in  size,  set  into  and  flush  with  the  top 
of  a  drawing  table.  Below  is  a  hopper-shaped 
box  of  wood  with  the  sides  at  45°  with  the  hori- 
zontal, painted  white.  Electric  lamps  are  placed 
in  the  bottom,  some  of  the  light  from  which  di- 
rectly illuminates  the  glass,  and  some  is  reflected 
upward  from  the  sloping  sides  of  the  box,  thus 
giving  an  even  illumination  to  the  whole  panel. 


usually  are  not  very  accurate.      The 


QoOoQcO 


n. 


Fig.  13. 


To  prevent  the  glass  from  getting  very  hot,  air  is  allowed  to  circulate  through  holes  in 
the  bottom  of  the  box  and  at  the  top  of  the  sides.     But  the  glass  gets  hot  enough  to  expand 


12  INSTRUMENTS   AND   THEIR   USE 

considerably,  and  should  not  be  made  to  fit  tightly  into  the  table.     One  side  of  the  box  should 
be  hinged  to  allow  access  to  the  lamps. 

By  the  use  of  the  copying  glass,  drawings  may  be  copied,  by  simply  tracing  on  paper 
through  which,  ordinarily,  the  lines  of  the  original  drawing  would  not  be  visible.  But  by 
illuminating  the  back  of  the  latter  its  lines  are  made  visible  through  very  thick  paper. 

14.  Straightedge.     A  necessary  implement  for  accurate  drawing  is  a  steel  straightedge. 
This  is  simply  a  strip  of  steel,  nickel  plated,  about  -^  inch  thick,  with  the  opposite  long  edges 
perfectly  straight  and  parallel.      Straightedges  vary  in  length  from  15  to  72  inches,  and  in 
width  from  1^  to  3  inches.     There  is  a  hole  near  one  end  for  hanging  the  instrument  up 
when  not  in  use,  —  a  precaution  which  should  not  be  neglected,  as  otherwise  the  edge  is  very 
likely  to  get  nicked,  or  the  steel  sprung  out  of  shape.     The  36-inch  length  is  probably  best 
suited  to  ordinary  work. 

The  straightedge  is  used  not  only  for  the  actual  drawing  of  long  lines,  but  also  as  a  base 
upon  which  a  triangle  is  worked. 

15.  Needle  Point  or  Pricker.     This  is  simply  a- fine  needle  held  in  any  convenient  handle. 
Dealers   sell   for   this  purpose  handles   having  a  socket  at  the  end  for  holding  the  needle. 
Usually,  however,  the  instrument  is  made  by  the  draftsman.     A  fine  needle  is  broken  so  that 
about  |  inch  of  the  pointed  end  remains.      This  is  grasped  in  a  pair  of  pinchers  and  the  blunt 
end  is  forced  into  the  end  of  a  stick  of  soft  wood  whittled  to  the  diameter  of  a  pencil,  leaving 
about  ^  inch  of  the  pointed  end  of  the  needle  exposed.     The  stick  is  then  tapered  at  the  needle 
end,  and  at  the  opposite  end,  for  about  two  thirds  of  its  length,  it  is  flattened  on  opposite  sides 


PAPER  13 

so  as  to  be  wedge  shaped ;  this  is  to  prevent  the  instrument  from  rolling  off  any  inclined  sur- 
face upon  which  it  may  be  placed.     The  handle  is  more  easily  kept  clean  if  it  is  shellacked. 

16.  Paper  Weights.     Various  forms  of  weights  for  holding  down  paper,  straight  edges, 
etc.,  are  sold.     A  very  neat  form  is  a  cylinder  of  lead  about  2|  inches  in  diameter  and  1  inch 
high.     This  is  inclosed  in  a  tin  case  which  is  covered  with  felt.     A  very  satisfactory  form  is 
more  simply  made  by  filling  canvas  bags  with  shot.     These  should  be  about  2|  inches  square, 
and  contain  about  3  pounds  of  shot. 

17.  Paper.     An  important  difference  in  papers  depends  upon  the  method  of  manufacture. 
Machine-made  paper  is  formed  by  an  endless  belt,  usually  of  cloth,  which  moves  through  a 
long  trough  containing  water  and  picks  up  the  cotton,  linen,  or  wood  fibers  which  are  sus- 
pended in  it,  and  of  which  the  paper  is  to  be  made.     The  currents  formed  by  the  belt  moving 
through  the  water  cause  most  of  the  fibers  to  be  arranged  on  the  belt  parallel  with  its  length. 
In  some  papers  the  imprint  of  the  weave  of  the  belt  may  be  seen  on  the  "  wrong "  side. 
When  paper  thus  made  is  dampened  it  behaves  much  as  a  board  does  when  wet,  and  for 
the  same  reason.     The  water  gets  between  the  fibres  (which  are  long  and  slender)  and  crowds 
them  apart.     Thus  the  paper  is  considerably  expanded  in  the   direction   perpendicular   to 
that  along  which  most  of  the  fibers  lie,  and  only  slightly   expanded  along  the  length  of 
the  fibers. 

In  hand-made  paper  the  fibers  cross  each  other  in  all  directions,  and  when  such  paper 
is  dampened,  it  expands  nearly  equally  in  all  directions,  and  is  therefore  especially  valuable 
for  fine  drawings. 


14  INSTRUMENTS  AND  THEIR  USE 

The  best-known  hand-made  paper  is  Whatman's.  The  sheets  are  sorted,  those  having 
imperfections  are  called  "  Retree,"  and  the  perfect  ones  "Selected  Best."  They  are  also 
classified  as  "Hot  Pressed,"  or  simply  "  H,"  and  "Cold  Pressed."  The  hot-pressed  sheets 
have  a  relatively  smooth  surface  on  which  a  fine  pen  can  be  used.  The  cold-pressed  sheets 
have  an  open,  fibrous  surface  especially  adapted  to  work  in  water  colors.  They  are  further 
classified  as  "  Not  Hot  Pressed,"  or  "  N,"  and  "  Rough,"  or  "  R,"  the  latter  being  a  very  heavy 
paper  with  a  decidedly  rough  surface  which  gives  a  beautiful  effect  to  color  washes  in  large 
areas. 

Large  sheets  of  Whatman  paper  are  thicker  than  small  ones,  and  for  color  work  on  small 
sheets  it  is  advisable  to  cut  large  sheets  into  pieces  of  the  desired  size. 

While  Whatman  paper  has  nominally  a  right  side,  as  shown  by  the  watermark,  yet  either 
surface  may  be  used. 

The  following  designations  of  sizes,  while  commonly  associated  with  Whatman  paper, 
are  applicable  to  all  other  papers  :  — 

Cap,  13  x  17  in.  Royal,  19  x  24  in.  Atlas,  26  x  34  in. 

Demy,  15  x  20  in.  Super  Royal,  19  x  27  in.         Double  Elephant,  27  x  40  in. 

Medium,  17  x  22  in.         Imperial,  22  x  30  in.  Antiquarian,  31  x  53  in. 

Other  papers  suitable  for  fine  line  work  are  Leonine,  Weston's  Linen  Record,  and  Keuffel 
&  Esser's  Normal.  Eggshell  paper  has  a  hard  surface  containing  slight  indentations,  and 
is  effective  if  lines  are  not  too  fine.  Keuffel  &  Esser's  Paragon  takes  water  colors 
fairly  well. 


PAPER  15 

Cross-section  Paper,  Fig.  19,  is  in  sheets  about  16  x  20  inches  and  in  rolls  20  inches  wide. 
The  best  sheets  are  printed  from  plates  ;  the  inferior  sheets  and  the  rolls  are  machine  ruled. 
The  surface  is  divided  into  squares  by  heavy  lines,  the  sides  of  the  squares  being  1  in.,  -^  ft.,  or 
1  centimeter.  These  squares  are  subdivided  into  smaller  squares  by  fine  lines,  each  side  being 
i'  TO'  iV  incn>  1^0  foot,  1  millimeter,  etc.  There  are  several  other  systems 'of  division  for 
special  purposes.  The  ruling  is  in  blue,  green,  or  orange,  the  latter  being  used  mostly  on 
thin  paper  for  blue  printing. 

For  topographical  work  the  paper  divided  into  -^  inch  squares  is  most  generally  useful. 
It  has  a  great  variety  of  uses,  the  most  common  of  these  in  topography  being  in  making  studies 
of  sloped  embankments  and  cuts,  and  in  showing  sections  of  grading  of  all  kinds.  When 
a  planimeter  is  not  at  hand,  cross-section  paper  is  sometimes  used  for  finding  areas  within 
irregular  outlines,  by  counting  the  squares  and  fractional  parts  of  squares  within  the  outline. 

This  paper  is  also  called  "  squared  "  and  "  quadrille  "  paper. 

Profile  paper  is  like  cross-section  paper  except  that  the  horizontal  and  vertical  divisions 
are  to  different  scales  ;  thus  the  surface  is  divided  into  rectangles  instead  of  squares.  "  Plate 
A  "  has  4  divisions  per  inch  horizontally  and  20  vertically.  The  corresponding  divisions  for 
"  Plate  B  "  are  4  and  30,  and  for  "  Plate  C  "  5  and  25.  The  ruling  for  Plate  A  is  shown  in 
Fig.  46.  This  paper  is  used  for  plotting  profiles  (Art.  107)  or  other  sections  where  the  differ- 
ences in  surface  elevation  are  slight.  Profile  paper  can  be  bought  in  sheets,  but  is  more  common 
in  rolls  20  inches  wide.  The  ruling  is  on  heavy  paper  in  green  or  orange,  and  on  tracing  paper 
in  orange. 

Transfer  paper  may  be  made  by  going  over  the  surface  of  thin  paper  with  a  very  soft 
pencil,  and  then  rubbing  with  a  chamois  stump  or  piece  of  blotting  paper  to  distribute  the 


16  INSTRUMENTS  AND  THEIR  USE 

"lead"  more  evenly;  or  the  pencil  may  be  ground  on  a  file,  and  the  filings  rubbed  over  the 
thin  paper.  This  paper  may  be  used  to  copy  drawings  that  are  made  on  fairly  thin  paper,  as 
described  in  Art.  143. 

Tracing  paper  is  thin,  translucent  paper  which  affords  a  means  for  making  copies  of 
drawings  rapidly  by  simply  tracing  the  lines.  This  paper  is  usually  deficient  in  strength  and 
in  erasing  qualities,  and  should  be  employed  only  for  studies  or  for  temporary  use.  It  is  sold 
in  rolls,  and  is  from  37  to  54  inches  wide. 

Tracing  cloth  is  a  prepared  muslin,  transparent,  and  very  strong.  It  is  used  in  the  same 
way  as  tracing  paper  except  that,  if  ink  is  to  be  used,  as  is  commonly  the  case,  the  surface 
must  be  rubbed  with  some  substance  to  remove  an  imperceptible  greasy  coating.  For  this 
purpose  common  chalk  dust  is  as  good  as  anything.  Either  side  of  the  cloth  may  be  used. 
Two,  or  even  three,  erasures  may  be  made  if  done  carefully  with  a  good  eraser.  A  knife 
should  not  be  used.  The  surface  is  left  rough  after  an  erasure,  and  will  soon  become  dirty  if 
left  in  that  condition.  To  restore  the  smoothness  scrape  a  little  dust  from  a  piece  of  talc  on 
the  rough  place  and  rub  it  in  briskly  with  a  clean  cloth. 

Pencil  marks  may  be  quickly  removed  by  rubbing  with  a  cloth  wet  with  benzine  or  gaso- 
line, which,  however,  will  not  injure  the  inked  lines.  (See  also  Art.  133.) 

18.  Pens  and  Holder.  A  variety  of  pens  will  be  needed.  No  list  can  easily  be  made  to 
suit  all  experienced  draftsmen,  but  the  following,  arranged  in  the  order  of  coarseness,  will  do 
for  the  beginner:  Gillott's  mapping  pen  No.  291,  Spencerian  epistolaire  No.  12,  Gillott's 
Nos.  170,  303,  404. 

The  penholder  should  be  not  less  than  |  inch  diameter  at  the  point  where  it  is  grasped  by 


BRUSHES  17 

the  fingers,  and  this  portion  of  it  is  best  made  of  cork.     A  holder  with  a  smooth,  metallic 
ferrule  at  the  lower  end  should  never  be  used. 

19.  Brushes.     For  color  work  two  brushes,  one  a  double-end  brush,  will  be  needed. 
The  best  round  camel  hair  brushes  in  albata  ferrules  are  recommended.     Finer  grades  are 
made  of  red  and  black  sable.     Suitable  sizes  are 

shown  in  Fig.  14.     (It  should  be  remembered 

that  a  full-size  drawing  of  an  object  looks  larger 

than  the  object.)     Brushes  are  numbered  ac-  £ 

cording  to  sizes,  but  the  numbering  is  not  stand- 

ard.     The  handles  should  preferably  be  simply  *"" 

polished,  not  painted.     Brushes  should  be  thoroughly  washed  in  clean  water  before  the  color 

can  dry  in  them,  and  laid  away  flat,  with  the  end  formed  straight  and  pointed. 

20.  Water  Glass.     The  best  form  of  water  glass  has  lips  on  opposite  sides  of  the  rim. 
These  furnish  a  convenient  place  for  laying  the  brush  when  it  is  temporarily  out  of  use.     A 
common  tumbler  should  also  be  provided  for  holding  water  in  which  to  clean  the  brushes. 

21.  Color  Saucers.     For  preparing  the  colors  a  "nest"  of  six  "cabinet"  saucers  about 
2|  inches  in  diameter  is  most  convenient.     These  saucers  fit  each  other  closely,  so  that  any 
saucer  may  serve  as  a  cover  for  another.     This  is  a  convenience  when  it  is  desired  to  protect 
the  colors  from  evaporation  for  a  time.     Select  saucers  which  are  decidedly  concave. 

22.  Colors.     The  most  convenient  pigments  for  color  work  are  the  moist  colors  in  porce- 
lain pans.     Those  made  by  Winsor  and  Newton  are  always  of  good  quality.     For  students' 
use  the  "  half  pans  "  will  be  found  large  enough. 


18  INSTRUMENTS  AND  THEIR   USE 

The  colors  should  include  Yellow  Ochre  (Y.O.),  Gamboge  (G.),  Crimson  Lake  (C.L.)^ 
Burnt  Sienna  (B.S.),  Prussian  Blue  (P.B.),  Payne's  Gray  (P.G.),  Sepia  (S.),  and  Burnt 
Umber  (B.U.).  Chinese  White  will  occasionally  be  found  useful.  The  tube  form  of  this 
pigment  is  preferable,  since  that  contained  in  pans  becomes  very  hard. 

23.  Colored  Pencils.  In  drafting  offices  considerable  use  is  found  for  colored  pencils  or 
"wax  crayons."  They  are  usually  known  by  number,  but  each  maker  uses  his  own  scheme 
of  numbering.  The  following  list  gives  a  fair  assortment,  the  numbering  being  that  of  A. 
W.  Faber  :  2,  yellow  ;  13,  blue  ;  30,  sienna  ;  38,  vermilion  ;  54,  purple  ;  62,  orange  ;  63,  light 
green  ;  69,  dark  green. 

For  uses  see  Art.  94. 


CHAPTER  II 


PRELIMINARY   PROBLEMS   AND   OPERATIONS 

24.  To  divide  a  given  distance  into  equal  parts.     The  usual  geometrical  construction  is 
shown  in  Fig.  15.     Let  it  be  required  to  divide  the  line  AB  into  five  equal  parts.     Draw 
AC  at  any  angle  with  AB,  and  from  A  lay  off  five  equal 

spaces  of  any  length,  and  connect  the  last  point,  5,  with  B. 
Parallels  to  5B  through  the  other  points  of  division  will 
intersect  AB  in  the  required  points. 

It  is  often  necessary  to  interpolate  the  number  of  equi- 
distant parallels  between  two  given  parallels,  as  in  draw- 
ing contours  for  slope  grading  (Art.  112).  If  the  given 
parallels  are  practically  straight  lines,  a  ready  means  of 
making  the  division  is  shown  in  Fig.  16.  Place  a  scale  of 
equal  parts  diagonally  across  the  lines  so  that  the  latter 
will  intercept  the  required  number  of  divisions  on  the 
scale  (5  in  the  figure),  and  place  a  point  close  to  the  edge 
of  the  scale  at  each  required  point  of  division. 

25.  To  divide  an  arc  into  equal  parts.     If  the  center 
of  the  arc  is  accessible,  a  protractor  may  be  used  to  lay 

19 


Fig.  16 


20 


PRELIMINARY  PROBLEMS  AND  OPERATIONS 


p.       .  - 


off  arcs  subtended  by  the  required  divisions,  and  lines  may  be  drawn  through  the  extremities 

of  the  protracted  arcs  and  the  center,  and  extended  to  the  given  arc. 

When  the  center  is  not  accessible,  the  following  method  may  be  used,  especially  if  the 

number  of  divisions  is  large.     Let  it  be  required  to  divide  arc  AB,  Fig.  17,  into  eight  parts. 

With  the  large  dividers  (or  a  scale  if  the  distances 
are  too  great  for  dividers)  lay  off  from  A  eight  equal 
parts,  1,  2,  ...  8,  such  that  8  falls  short  of  B.  With 
the  small  dividers  find  by  trial  |  of  the  distance  8  B, 
and  lay  this  off  once  from  1,  twice  from  2,  etc.,  giving 

the  points  1',  2',  ...  8',  which  are  the  required  points  of  division.     This  method  requires 

less  time,  and  injures  the  paper  less  than  would  be  the  case  if  the  whole  arc  were  divided  by  a 

series  of  trial  openings  of  the  large  dividers. 


26.  To  find  points  on  an  arc  of  large 
radius.  It  is  sometimes  impossible  or  in- 
convenient to  draw  a  circular  arc  of  large 
radius  with  beam  compasses  or  a  railroad 
curve.  The  arc  may  otherwise  be  drawn 
by  finding  a  number  of  its  points  and  join- 
ing them.  In  Fig.  18  let  AB  be  a  chord 
of  the  required  arc  of  radius  R. 


B 


IAB 

sine  =  ^— — . 


Fig.  18. 
Draw  AO  and  B6,  each  making  with  AB  an  angle  whose 

These  lines  are  tangents  of  the  required  arc.     From  A  and  B  as  centers,  with 


EATING  THE   PLANIMETER  21 

radius  AB,  describe  arcs  cutting  the  tangents  in  0  and  6.  Divide  the  arcs  into  any  number  of 
equal  parts,  as  6,  and  number  them  in  reverse  order  from  the  chord,  as  shown.  The  intersec- 
tions of  Al  with  Bl,  A2  with  B2,  etc.,  will  give  points  on  the  required  arc.  These  may  be 
joined  either  by  means  of  a  ship  curve,  or  by  the  use  of  a  railroad  curve  which  closely  approxi- 
mates the  arc,  or  by  springing  a  steel  straightedge  (held  edgewise  to  the  paper)  so  that  it 
passes  through  the  points. 

27.  Multiplier  for  Planimeter  Measurements.     In  the  use  of  the  planimeter  as  described 
in  Art.  11,  the  instrument  measures  the  number  of  square  inches  of  paper  included  within  the 
boundaries  of  the  drawing.     But  the  relation  between  this  area  and  the  area  of  the  surface 
represented  by  the  drawing  obviously  depends  upon  the  scale  of  the  drawing.     If,  for  instance, 
the  scale  is  1  inch=  40  feet,  each  square  inch  of  drawing  represents  40x40  =  1600  square  feet 
of  surface  represented,  and  the  planimeter  record  of  total  area  in  square  inches  should  be  multi- 
plied by  1600  to  obtain  the  area  in  square  feet  of  the  surface  represented.     The  constant  multi- 
plier, then,  is  the  square  of  the  number  of  linear  feet  represented  by  one  linear  inch  on  the 
drawing. 

Find  the  multipliers,  to  obtain  square  feet,  for  the  following  scales:    1  inch  =80  feet, 
1  inch  =  3  rods,  3  inches =1  foot,  -^  inch  =  l  foot. 

28.  Rating  the  Planimeter.     In  the  form  of  planimeter  shown  in  Fig.  11,  the  graduated 
arm  G  can  be  slid  in  the  sleeve  S,  so  that  the  distance  WT  can  be  changed.     Sometimes  the 
arm  G,  instead  of  being  divided  into  many  equal  parts,  as  shown,  has  marks  upon  it  corre- 
sponding to  the  various  scales  ordinarily  used  in  making  plans.     The  appropriate  mark,  when 
set  against  a  scratch  shown  in  the  opening  at  the  end  of  S,  will  enable  the  instrument  to  be 


22 


PRELIMINARY  PROBLEMS  AND  OPERATIONS 


17 


used  without  the  multiplier  explained  in  the  last  article.  While  this  is  a  convenience,  it  is  not 
an  advisable  method  of  graduating  the  arm,  because  in  time  the  wheel  W  becomes  worn  so  that 
its  circumference  is  sensibly  changed,  and  a  corresponding  change  must  be  made  in  the  distance 
WT  to  compensate  for  the  wear. 

The  determination  of  the  proper  setting  of  the  arm  with  reference  to  the  index  mark  on 
the  sleeve  is  called  "rating  the  planimeter." 

A  method  of  rating  may  be  explained  by  reference  to  Fig.  19.     A  square  of,  for  instance, 
4  inches  on  a  side,  is  first  very  accurately  drawn  on  a  smooth  sheet  of  paper.      The  arm  of 

the  instrument  is  set  at  random  and  the  tracing  point  is 
passed  very  carefully  around  the  sides  of  the  square. 
Suppose  the  setting  of  the  arm  to  have  been  144  and  the 
reading  of  the  wheel  15.7.  Now,  as  shown  in  the  figure, 
plot  the  144  as  abscissa  and  the  15.7  as  ordinate,  and 
thus  obtain  point  A.  Make  another  setting  of  the  arm, 
obtain  another  reading  for  area,  and  plot  the  results  as 
before,  obtaining  the  point  B.  These  results  show  that 
the  arm  is  still  too  short,  as  both  readings  for  area  are 
less  than  16,  the  true  area  of  the  square.  Use  other  set- 
tings of  the  arm,  some  of  which  shall  give  area  readings 
of  more  than  16.  Draw  a  straight  line  AC  among  the 


° 


Setting  on  Arm. 
Fig.  19. 


points  thus  plotted.  The  horizontal  line  through  16  (the  true  area  of  the  square)  intersects 
AC  at  D.  From  D  draw  the  vertical  DE.  This  cuts  the  base  line  at  148.3  which  is  the  re- 
quired setting  of  the  arm. 


STRETCHING  PAPER  23 

Squares  of  other  sizes  may  be  used  to  get  additional  determinations  (which  should  be 
substantially  like  the  first),  and  the  mean  of  results  taken  as  the  true  setting.  If  any  one 
result  is  widely  at  variance  with  others,  it  indicates  an  error  in  drawing  the  square. 

A  variation  of  this  method  consists  in  measuring  a  circle  instead  of  a  square.  This  can 
best  be  done  as  follows  :  near  each  end  of  a  strip  of  firm  cardboard  prick  a  fine  hole,  the  dis- 
tance between  the  holes  being  carefully  determined.  Through  one  of  these  pin  the  strip  down 
to  a  sheet  of  smooth  paper  on  the  drawing  board,  by  a  short  piece  broken  from  a  fine  needle. 
Place  the  tracing  point  of  the  planimeter  in  the  other  hole  and  cause  the  strip  to  rotate  about 
the  needle.  The  tracer  will  thus  be  made  to  traverse  the  circumference  of  a  circle  whose 
radius  is  the  distance  between  the  holes,  and  whose  area  can  be  computed.  Some  instruments 
are  supplied  with  a  strip  of  metal  to  be  used  as  here  indicated  for  the  cardboard. 

The  anchor  point  P,  Fig.  11,  should  be  so  placed,  relative  to  the  figure  to  be  measured, 
that  the  point  T  need  not  be  brought  very  near  to  it  in  traversing  the  boundary,  otherwise  the 
instrument  will  not  stand  firmly. 

It  is  sometimes  found  that  with  the  anchor  point  in  different  positions  relative  to  the 
boundary  of  the  figure  different  areas  are  obtained.  This  indicates  a  lack  of  adjustment  in 
the  parts,  and  the  instrument  should  be  sent  to  the  maker  for  adjustment. 

29.  Stretching  Paper.  Paper  upon  which  any  considerable  amount  of  water  coloring  is  to 
be  done  must  be  stretched,  otherwise  the  moisture  of  the  colors  will  cause  it  to  wrinkle  or 
"  cockle,"  and  the  color  will  not  dry  smoothly. 

Lay  the  sheet  to  be  stretched  face  upward  upon  a  larger  sheet  of  clean  manila  paper  and 
with  a  soft  sponge  and  clean  water  dampen  the  surface.  Turn  the  paper  over  and  dampen  the 


24  PRELIMINARY  PROBLEMS   AND   OPERATIONS 

back  to  the  edges,  uniformly  and  thoroughly.  When  it  lies  perfectly  limp,  take  up  as  much 
water  as  possible  from  the  margins,  with  the  sponge  squeezed  dry,  and  spread  glue  or  strong  mu- 
cilage thinly  for  a  width  of  |-  inch  around  the  edges.  Place  the  sheet  with  the  glued  surface 
downward  upon  the  drawing  board,  and  press  the  edges  downward  and  gently  outward 
till  the  sheet  is  smooth.  With  a  smooth,  blunt  object,  such  as  the  end  of  a  knife  handle, 
rub  the  edges  down,  using  as  much  pressure  as  the  dampened  paper  will  bear. 

Meanwhile  keep  the  paper  expanded  by  more  water,  but  be  careful  not  to  go  within 
an  inch  or  more  of  the  edges,  otherwise  the  glue  will  be  prevented  from  hardening.  The 
board  must  be  perfectly  level  so  that  the  water  on  the  surface  will  not  run  to  the  edges. 

Continue  to  rub  down  the  edges  and  to  keep  the  paper  expanded  till  the  glue  has 
firmly  set.  Take  up  any  superfluous  water  and  allow  the  sheet  to  dry,  still  in  a  horizontal 
position. 

On  first  dampening  the  paper  the  surface  may  be  gently  rubbed  with  the  sponge,  but 
after  that  it  should  be  patted. 

It  is  a  mistake  to  suppose  that  a  great  deal  of  water  is  needed  to  expand  the  paper,  as 
will  be  seen  when  it  is  remembered  that  a  very  noticeable  expansion  is  caused  by  the  moisture 
in  the  air  on  a  damp  day. 

The  drawing  board  for  stretching  paper  should  be  shellacked,  as  this  prevents  the  paper 
from  being  stained  by  the  wood,  and  prevents  the  glue  from  sinking  into  the  grain,  with 
the  probable  result  that  some  portions  of  the  edges  will  not  be  well  secured.  Old,  weather- 
stained  wood  is  sure  to  leave  brown  stains  which  cannot  be  removed. 

Care  must  be  exercised  that  the  paper  is  not  glued  to  the  board  at  any  point  except 
at  the  edges. 


MOUNTING  PAPER   ON  CLOTH  25 

30.  Mounting  Paper  on  Cloth.  The  durability  of  a  drawing  is  much  increased  by 
applying  a  backing  of  cloth.  Whatman  and  some  other  papers  grow  tender  with  age,  and 
should  be  backed  with  cloth,  or  "mounted,"  if  they  are  to  be  subjected  to  much  handling. 
It  is  better  to  mount  the  paper  before  the  drawing  is  made,  especially  if  water  coloring  is 
to  be  done.  Lithographs,  photographs,  blueprints,  in  fact  all  sorts  of  drawings,  prints, 
and  engravings  are  mounted  to  make  them  more  available  for  continued  use. 

Only  bleached  cotton  cloth  is  used  for  mounting.  The  piece  should  be  at  least  an  inch 
larger  all  around  than  the  paper.  With  small  tacks  fasten  the  cloth  to  the  drawing  board, 
beginning  always  at  the  middle  of  a  side,  and  working  equally  each  way.  Tack  down  the 
long  edges  first,  and  pull  the  cloth  in  each  direction  with  a  force  a  little  greater  than  enough 
to  make  it  simply  smooth.  Expand  the  paper  by  moisture,  apply  starch  paste  (never  muci- 
lage or  glue)  to  its  back,  and  lay  carefully  face  up  on  the  cloth.  Press  it  down  with  a  rubber 
roller,  or  (after  having  covered  it  with  another  sheet  of  cloth  or  paper)  with  the  flat  of  the 
hand.  In  either  case  begin  at  the  center  and  work  toward  the  edges  so  'that  all  air  shall 
be  pressed  out. 

Since  the  whole  of  the  back  is  covered  with  paste,  it  is  not  necessary  to  keep  the  paper 
expanded  till  the  paste  dries.  Be  careful  to  apply  plenty  of  paste  to  the  edges  of  the  paper. 
If  the  paper  is  thin,  the  paste  alone  will  expand  it. 

It  is  a  wise  precaution  to  lay  a  single  thickness  of  newspaper  between  the  cloth  and  the 
drawing  board,  otherwise  the  paste  will  sometimes  strike  through  the  cloth  in  spots,  and  cause 
it  to  stick  to  the  board,  thus  producing  a  wrinkled  area  in  the  finished  work. 

Paste  suitable  for  mounting  paper  may  be  made  as  follows:  to  one  fourth  cupful  of  com- 
mon laundry  starch  add  as  much  flour  as  will  be  contained  in  the  interstices  of  the  lumps  ; 


PRELIMINARY  PROBLEMS  AND  OPERATIONS 


add  a  very  little  cold  water,  —  only  enough  to  make  a  paste  of  the  starch  and  flour,  and  with 
the  back  of  a  spoon  grind  the  paste  smooth  ;  then  add  enough  more  cold  water  to  thin  the 
paste  so  that  it  will  run  freely  from  the  cup.     Three  cupfuls  of  water  should  meanwhile  have 
been  brought  to  the  boiling  point  in  an  open  saucepan.     Still  keeping  the  saucepan  over  the 
fire,  pour  the  paste  slowly  into  the  boiling  water,  and  stir  very  briskly  with  a  spoon.    Let  the 
mixture  boil  for  a  minute  or  two,  then  set  the  pan  into  a  large  dish  into  which  cold  water  is 
allowed  to  run.     While  the  paste  is  thus  cooling,  stir  it  slowly  to  prevent  the  formation  of  a 
______^_____^^^____       hard  coating  on  top. 

A  flat  bristle  brush  is  best  for  spreading  the  paste, 
which  should  be  applied  liberally  and  evenly.  -The  quan- 
tity here  given  is  sufficient  for  about  thirty-six  square 
feet  of  paper. 


31.  Splicing  Paper.  It  is  often  necessary  to  join  two 
or  more  pieces  of  paper,  especially  when  mounting  on  cloth. 
If  the  edges  of  the  sheets  are  simply  lapped,  the  joint  will 
be  clumsy,  particularly  if  the  paper  is  thick;  but  if  the 
edges  are  first  beveled,  a  better  joint  will  be  secured. 

Beveling  may  be  done  as  follows:  lay  the  paper  on  a 
smooth,  hard  surface  (glass  is  best),  and  with  a  sharp- 


Fig.  20. 


pointed  knife  cut  along  a  straight  edge  where  the  edge  of  the  sheet  is  to  be.  This  cut  must 
extend  only  through  the  "  skin  "  of  the  paper,  and  should  be  of  equal  depth  in  every  part. 
Turn  the  sheet  over  and  tear  off  the  edge,  holding  it  in  relation  to  the  sheet  as  shown  in  Fig.  20. 


PATCHING  TRACING  CLOTH  27 

The  thickness  of  the  thin  edge  of  the  beveled  portion  will  be  determined  by  the  depth  of  the 
cut,  and  the  width  of  the  bevel  will  depend  upon  the  angle  at  which  the  edge  of  the  marginal 
strip  is  held  relative  to  the  edge  of  the  sheet  while  the  tearing  is  in  progress  ;  the  more 
nearly  parallel  the  edges  are,  the  less  will  be  the  width  of  the  bevel.  Of  the  two  sheets 
which  are  to  be  lapped  at  their  beveled  edges,  the  one  which  overlaps  should  have  the  cut  on 
the  right  side,  while  the  one  which  underlaps  should  have  it  on  the  wrong  side.  If  the  lap  is 
greater  than  the  width  of  the  bevel,  the  torn  surfaces  will  be  completely  hidden. 

The  tearing  should  be  practiced  on  a  waste  piece  of  paper  of  the  same  kind  as  the  sheets 
to  be  joined. 

32.  Patching  Tracing  Cloth.  Tracing  cloth  will  not  stand  a  great  deal  of  erasing,  and 
if  more  than  one  erasure  is  made  at  the  same  place,  the  cloth  often  breaks.  Such  a  rent  should 
be  patched.  With  an  ink  eraser  clean  the  back  of  the  tracing  for  a  short  distance  from  the 
edges  of  the  rent.  Have  ready  a  piece  of  tracing  paper  considerably  larger  than  the  desired 
patch.  With  the  end  of  the  ringer  rub  paste  evenly  and  thinly  over  the  area  of  the  cloth 
cleaned  with  the  eraser,  apply  the  tracing  paper,  and  rub  it  down.  When  the  paste  is 
thoroughly  dry,  tear  away  the  superfluous  paper  on  a  bevel  as  described  in  the  last  article. 
In  this  case  the  outline  of  the  patch  is  an  irregular  line  defined  by  the  edge  of  the  pasted 
area,  instead  of  a  knife  cut. 

Blueprints  made  from  a  patched  tracing  will  show  lighter  blue  where  the  patch  occurs, 
but  the  beveled  edge  of  the  patch  causes  the  outline  of  this  lighter  area  to  be  indistinct. 


CHAPTER   III 

PLOTTING 

33.  The  General  Problem.     The  object  of  plotting  is  to  transcribe  to  paper,  to  a  suitable 
scale,  such  data  as  are  necessary  to  convey  clearly  certain  ideas  concerning  areas  of  the  earth's 
surface     and    surveys   which    may   have   been    made     upon    it.      These    data    include   the 
following  :     the  boundary  lines  of  the  portion  of  land  under  consideration  ;  such  arbitrary 
lines  as  may  have  been  used  in  the  survey  ;  the  imaginary  lines  joining  certain  points  of  equal 
elevation  (i.  e.  contours,  Art.  109)  ;  and  a  representation  of  the  natural  and  artificial  features 

-  bodies  of  water,  trees,  buildings,  etc. — that  occur  within  the  boundary.     Not  all  of  these 
are  shown  in  each  instance,  the  purpose  of  the  drawing  determining  the  amount  of  detail. 

The  process  of  locating  these  lines  and  objects  in  their  proper  magnitudes  and  relations  is 
called  plotting. 

34.  Plotting  a  Triangulation.     Every  figure  whose  boundaries  are  composed  of  straight 
lines  may  be  divided  into  triangles  ;  and  one  of  the  most  accurate  field  methods  of  determin- 
ing the  relative  positions  of  points  on  the  earth's  surface  is  by  triangulation.     By  this  process 
the  objects  to  be  plotted  are  made  the  vertices  of  triangles,  the  angles  of  which  are  measured 
very  accurately,  and  the  lengths  of  whose  sides  are  computed, —  except  the  first  side,  or  base, 
of  a  series  of  triangles,  which  is  measured.     The  most  direct  way  of  plotting  such  triangles  is 

28 


PKOTRACTING  AN  ANGLE  29 

by  first  laying  down  the  base  line  to  scale,  and  from  its  ends  swinging  intersecting  arcs  with 
radii  respectively  equal  to  the  other  two  sides  of  the  triangle,  thus  locating  the  vertex  opposite 
the  base.  The  sides  of  this  triangle  may  in  turn  serve  as  bases. 

35.  Plotting  Progressive  Angles.     More  commonly  the  lines  to  be  plotted  run  as  consecu- 
tive sides  of  a  polygon,  whose  sides  have  been  measured  and  the  angles  between  which  are 
known.     In  plotting  these  the  sides  may  be  scaled  on  the  paper  and  the  angles  laid  down  in 
their  order.     The  more  difficult  part  of  this  process  is  the  plotting  of  the  angles,  for  which 
some  methods  are  given  below. 

36.  Protracting  an  Angle.     If  extreme  accuracy  is  not  required,  the  angle  may  be  laid  off  by 
means  of  a  protractor  (Art.  9),    as  this  is   the  quickest  and  most  convenient  method.     Draw 
to  scale  the  first  side  of  the  angle,  and  if  this  is  not  as  long  as  the  radius  of  the  protractor, 
extend  it  backward  from  the  end  where  the  vertex  of  the  angle  is  to  be;  also  extend  it  forward 
from  the  last-named  point  a  distance  slightly  greater  than  the  radius  of  the  protractor.    Place  the 
protractor  upon  this  line  with  its  diameter  coincident  with  it,  and  its  center  at  the  vertex 
point.     If  the  protractor  is  simply  a  graduated  arc,  prick  off  the  required  angle  at  its  edge, 
and  join  this  point  with  the  vertex  point  for  the  second  side  of  the  angle  ;  if  it  is  a  vernier 
protractor,  turn  off  the  required  angle  with  the  arm  and  draw  a  fine  line  along  the  latter,  and 
extend  this  line  to  the  vertex  point. 

The  angle  may  be  turned  off  on  the  vernier  protractor  either  before  or  after  setting  it 
on  the  line ;  but  in  either  case  see  that  the  protractor,  as  a  whole,  and  the  arm  are  properly 
placed  before  drawing  the  line  along  the  arm. 


30  PLOTTING 

37.  To  plot  an  Angle  by  its  Tangent.     This  method  is  suitable  for  plotting  angles  of  less 
than  45°  and  more  than  135°.     Acute  angles  are  plotted  directly,  and  obtuse  angles  are  ob- 
tained by  plotting  their  supplements. 

Let  it  be  required  to  plot  an  obtuse  angle  a,  Fig.  21,  one  side  of  which  is  AB.     Extend 

AB  to  C,  BC  being  a  measured  distance.  On  the  perpendicular 
CD  lay  off  CE  =  BC  x  tan  (180°  -a),  and  draw  EB  for  the  sec- 
ond side  of  the  angle. 

A  convenient  length  for  BC  is  10  inches,  for  if  a  table  of 
natural  tangents  be  used,  the  value  of  CE  is  obtained  at  once  by 
moving  the  decimal  point  one  place  to  the  right.  For  very  accu- 
rate work,  however,  a  greater  length  is  advisable. 

38.  To  plot  an  Angle  by  the  Chord  of  its  Subtended  Arc.     When  the  angle  to  be  plotted 
directly  is  greater  than  45°,  the  method  here  given  is  preferable  to  that  given  in  the  last 

article. 

In  Fig.  22  let  AB  be  one  side  of  the  required  angle  a.  With  radius 
AC  describe  an  indefinite  arc  from  A  as  center.  From  C  as  center  describe 
arc  DE  intersecting  the  first,  the  radius  R  of  DE  being  found  by  the  equa- 
tion R  =  2  f  AC  x  sin-  J.  Join  the  intersection  of  the  two  arcs  with  A  for 
the  second  side  of  the  required  angle. 

39.  Defect  of  Plotting  Progressive  Angles.     The   defect  of   the  method  of  progressive 
angles  is  that  the  position  of  any  line  of  the  polygon  depends  directly  upon  that  of  previous 


DEFLECTION  ANGLE  31 

sides;  thus  an  error  in  any  side  is  carried  into  all  succeeding  sides.  If  the  sides  form  a  closed 
figure,  the  error  will  be  detected  by  the  failure  of  the  plot  to  "close,"  and  all  the  work  suc- 
ceeding the  point  at  which  the  error  occurred  must  be  corrected.  If  the  courses  do  not  form 
a  closed  figure,  the  error  may  escape  detection. 

It  is  obvious  that  it  is  desirable  to  plot  by  methods  which  shall  confine  the  effects  of  an 
error  to  the  course  wherein  the  error  is  made.  The  following  methods  are  designed  to  attain 
such  a  result,  as  well  as  to  provide  a  high  degree  of  accuracy. 

40.  Deflection  Angle.  The  angles  to  be  dealt  with  in  plotting  will  depend  upon  the 
method  pursued  in  the  survey.  If  it  is  a  small,  closed  polygon  that  has  been  surveyed,  it  is 
probable  that  the  deflection  angle  between  the  sides  or  "courses"  will  have  been  measured. 
This  angle  is  the  one  between  one  course  extended  beyond  the  angle  point  and  the  following 
course.  Thus  in  Fig.  21  the  angle  EEC  is  the  deflection  angle  between  courses  AB  and  BE. 
The  interior  angles  (a  in  Fig.  21)  are  the  supplements  of  the  corresponding  deflection  angles, 
and  a  proof  of  the  accuracy  of  the  measurements  for  a  closed  polygon  of  n  sides  is  that  the 
sum  of  the  interior  angles  shall  be  180°  taken  as  many  times,  minus  two,  as  the  figure  has 
sides;  or,  sum  of  interior  angles  =  (/» —  2)  180°.  Since  at  each  angle  of  a  polygon  the  interior 
and  deflection  angles  together  equal  180°,  the  total  of  such  angles  is  n  x  180°;  but  since  the 
total  of  the  interior  angles  is  (n  —  2)  180°,  the  sum  of  the  deflection  angles  =  (n  x  180°)  —  (n  x 
180°—  2  x  1 80°)  =  360°,  whatever  the  value  of  n  ;  and  this  furnishes  a  ready  check  upon  the 
field  work.  This  is  not  true,  however,  when  there  are  reentrant  angles,  as  at  C,  Fig.  24. 

Deflection  angles  are  right  (marked  simply  r),  or  left  (l~),  depending  upon  their  position 
with  respect  to  the  first  side  produced.  Thus  in  Fig.  21  the  deflection  angle  EBC  is  Z, 


32  PLOTTING 

since  it  lies  to  the  left  of  AB  produced.  In  Fig.  24  all  deflection  angles  are  r  except  that 
at  C.  But  if  we  go  around  the  figure  in  the  direction  contrary  to  that  indicated  by  the 
order  of  the  letters,  all  deflection  angles  are  I  except  that  at  C. 

41.  Bearings.  When  the  survey  is  made  with  a  magnetic  compass,  the  bearings  of  the 
courses  are  taken,  that  is,  the  acute  angles  which  the  several  courses  make  with  the  magnetic 
north  and  south  line.  The  bearings  of  courses  should  not  be  written  indiscriminately  ;  in 
Fig.  23  it  is  seen  that  the  bearing  of  BC  may  be  written  N  74°  E  with 
reference  to  the  meridian  through  B,  or  it  may  be  written  S  74°  W  with 
reference  to  the  meridian  through  C.  In  writing  the  bearings  it  should  be 
assumed  that  the  survey  proceeded  consecutively  in  one  direction,  and  the 
bearing  of  each  course  should  then  be  with  reference  to  the  meridian 
through  its  point  of  beginning. 

Of  course  the  bearings  may  be  given  with  reference  to  the  true  merid- 
ian rather  than  the  magnetic,  and  the  plan  should  indicate  which  meridian 
is  used.     This  is  usually  done  by  drawing  a  north  point  and  marking  it 
"  True  Meridian  "  or  "  Magnetic  Meridian,"  as  the  case  may  be. 

It  is  not  necessary  that  the  actual  bearings  of  all  courses  be  determined  in  the  field,  for  if 
the  bearing  of  one  course  be  known,  the  bearings  of  the  other  courses  may  easily  be  determined 
by  a  proper  use  of  the  deflection  or  included  angles  between  courses.  Thus  in  Fig.  23,  know- 
ing the  bearing  of  BC  to  be  N  74°  E,  find  the  interior  angles  and  the  bearings  of  the  other 
courses  from  the  following  deflection  angles,  beginning  at  C  and  proceeding  in  right-hand 
order  :  91°,  82°,  80°,  68°,  39°. 


TOTAL   LATITUDES   AND   LONGITUDES  33 

A  survey  may  be  made  without  reference  to  either  the  magnetic  or  true  meridian,  and 
for  purposes  of  plotting  and  computation  of  area  the  bearings  of  the  courses  may  be  found 
with  reference  to  one  of  the  sides  or  to  an  arbitrarily  chosen  line,  this  line  then  being 
used  as  if  it  were  really  a  meridian.  Bearings  thus  computed  from  an  assumed  reference 
line  are  called  false  bearings.  Some  labor  is  saved  by  using  one  of  the  courses  as  the  assumed 
meridian. 

42.  Azimuth.     The  azimuth  of   a  course  is  the  total  angle  which  it   makes  with  the 
meridian,  whether  this  angle   is  acute  or  obtuse.      There  is  no  general  agreement  among 
surveyors  as  to  whether  the  azimuth  should  be  read  from  the  south  by  way  of  west,  north, 
and  east ;  or  from  the  north  in  the  same  direction.     Of  course,  in  a  single  survey  one  or 
the  other  of  these  methods  should  be  adhered  to.     In  Fig.  23,  if  readings  are  made  from 
the  north,  the  azimuth  of  BC  is  74°;  if  from  the  south,  it  is  180° +  74°  =  254°.     It  will  be 
seen  that  there  are  relations  between  interior  angle,  deflection  angle,  bearing,  and  azimuth  such 
that  if  the  directions  of  courses  be  given  by  any  one  of  these  methods,  their  directions  may 
be  expressed  by  any  other  method,  though   it   may  be   necessary  to  use  false  bearings  or 
azimuths. 

43.  Plotting  by  Total  Latitudes  and  Longitudes.     This  is  an  excellent  method  for  several 
reasons,  viz.    that  great  accuracy  is  possible ;  an  error  in  plotting  one  course  is  not  carried 
into  succeeding  courses  ;  few  auxiliary  lines  are  needed,  and  these  do  not  cover  a  large  area 
outside  that  required  for  the  finished  plot. 

For  illustration  let  the  following  notes  of  a  closed  polygon  of  6  sides  be  considered  :  — 


34 


PLOTTING 


COURSE 

LEN<;TH,  FKET 

BEARING 

AB 

1070.00 

S.  72°  -20'    E. 

BC 

845.40 

S.  32°  -40'  W. 

CD 

482.00 

S.  35°  -20'    E. 

DE 

1107.00 

S.  71°  -50'  W. 

EF 

1216.68 

N.  29°  -29'  W. 

FA 

1080.00 

N.  48°  -30'  E. 

A  free-hand  sketch  of  this,  Fig.  24,  shows  that  the  most  westerly  point  occurs  at  F,  the 
junction  of  EF  and  FA.    This  fact  also  appears  from  an  inspection  of  the  bearings  in  the  table. 

If  through  F  a  meridian  NS  and  a  horizontal  line  (parallel  of  lati- 
tude) FG  be  drawn,  these  lines  will  be  axes  from  which  the  corners  of 
the  polygon  may  most  conveniently  be  plotted. 

The  table  of  latitudes  and  longitudes  given  below  is  next  computed. 
This,  in  practice,  may  be  an  extension  of  the  table  given  above.  Since 
the  plotting  will  be  done  from  axes  through  F,  course  FA  is  the  first  one 
used  in  making  columns  4  and  5.  The  total  latitude  of  a  point  is  simply 
the  distance  of  the  point  above  or  below  the  axis  FG,  and  the  total  longi- 
tude is  the  distance  to  the  right  of  the  meridian  through  F;  hence,  begin- 
ning with  FA,  the  total  latitude  and  longitude  of  A  are  the  same  as  the 
latitude  and  longitude  respectively  for  course  FA,  and  the  total  latitudes  and  longitudes  of 
the  successive  points  B,  C,  D,  etc.,  are  obtained  by  adding  algebraically  the  successive  latitudes 
and  longitudes,  beginning  with  course  FA  as  indicated. 


Fig.  24. 


SURVEYS   BASED  ON  A   SYSTEM   OF   COORDINATES 


35 


The  proof  of  the  correctness  of  the  last  two  columns  is  that  the  total  latitude  as  well  as 
the  total  longitude  of  point  F  (the  forward  extremity  of  EF)  is  zero,  as  it  should  be,  since  the 
point  is  at  the  intersection  of  the  axes. 


COURSE 

LATITUDE 
Length  of  Course 
x  cos  Bearing 

LONGITUDE 
Length  of  Course 
x  sin  Bearing 

TOTAL 
Lat. 

TOTAL 
Lon. 

AB 

-  324.72 

+  1019.30 

+     390.91 

1828.17 

BC 

-  711.68 

-    456.30 

-    320.77 

1371.87 

CD 

-  393.21 

+    278.76 

-    713.98 

1650.63 

DE 

-  345.14 

-  1051.82 

-  1059.12 

598.81 

EF 

+  1059.12 

-    598.81 

0.00 

0.00 

FA 

+  715.63 

+    808.87 

+    715.63 

808.87 

To  make  the  final  plot  two  axes  are  drawn  accurately  perpendicular  to  each  other,  corre- 
sponding to  NS  and  FG  of  Fig.  24  ;  the  vertices  of  the  polygon  are  then  fixed  by  using  the 
distances  in  the  last  two  columns  as  coordinates  ;  A,  for  instance,  being  715.63  feet  above 
FG  and  808.87  feet  to  the  right  of  NS.  The  minus  signs  attached  to  some  total  latitudes 
now  indicate  simply  that  they  lie  below  FG. 

Any  other  point  than  F  might  have  been  chosen  through  which  to  draw  the  axes.  If 
E  had  been  thus  used,  all  the  total  latitudes  would  have  been  plus,  while  some  total  longitudes 
would  have  been  plus,  and  some  minus. 

44.  Surveys  based  on  a  System  of  Coordinates.  In  extended  surveys  the  area  is  often 
divided  into  squares  whose  sides  may  be  from  50  feet  to  several  hundred  feet  in  length 


36 


PLOTTING 


according  to  the  magnitude  of  the  work.     The  origin  is  some  prominent  point,  such  as  the 

center  of  the  dome  of   City  Hall,  and  the  sides  of   the  squares  run  north  and  south,  and 

east  and  west. 

The  corners  of  at  least  some  of  these  squares  are  actually  located  on  the  ground,  and 

the  computed  position  of  points  of  a  survey  in  the  neighborhood  of  such  a  marked  corner 

may  be  verified  by  independently  locating  it  from  the  corner. 

In  plotting  such  a  survey  the  points  are  located  from  the 
sides  of  the  squares  in  which  they  lie  ;  thus  an  error  made  in 
locating  one  point  is  not  carried  into  the  location  of  the  suc- 
ceeding points,  and,  as  in  the  method  of  Art.  43,  all  the  work 
is  done  by  scaling  lineal  distances,  and  does  not  involve  laying 
down  any  angles  as  such. 

In  Fig.  25  suppose  that  AB  is  2128.3  feet  long,  that  it 
makes  an  angle  of  32°-15'  with  the  true  meridian,  and  that  the 
coordinates  of  A  are  18,627  N,  and  7314  W.  By  computing 
AC  and  BC  and  adding  them  (algebraically)  to  the  coordinates 
of  A,  the  coordinates  of  B  are  found  to  be  20,426.96  N,  and 
6178.31  W. 


c 

B 

1 
1 
1 

A 

000  N 

D    / 

E 

1 

/ 

j-jfl 

/ 

i 

/ 

i     / 

19 

000  N 

5 

(16627  N    J/ 
i  7JI4W    °A  S 

• 
<^ 

oc 

O 

8 

c 
m 

18 

000  N 

.  25. 

B  may  now  be  laid  off  426.96  feet  above  the  20,000-codrdinate  and  178.31  feet  to  the 
left  of  the  6000-coordinate. 

If  some  corner,  as  D  or  E,  not  far  distant  from  B,  be  marked  on  the  ground,  the  surveyor 
may  easily  determine  the  coordinates  of  B  by  observations  from  such  a  corner  and  thus  check 
the  work  above  described. 


PLOTTING   SURFACE  MARKINGS  37 

45.  Plotting  Surface  Markings.  The  locations  of  trees,  shore  lines  of  streams,  points  on 
contour  lines,  etc.,  do  not  need  to  be  located  with  the  extreme  accuracy  which  would 
demand  one  of  the  above  methods  of  plotting  ;  and  as  there  are  often  large  numbers  of  these 
surface  markings  to  be  plotted,  a  method  which  is  at  the  same  time  rapid  and  reasonably  ac- 
curate is  desirable.  These  "  side  shots  "  are  usually  made  in  the  field  by  the  stadia  method  ; 
that  is,  the  transit  is  set  at  the  forward  end  of  a  previously  determined  line  (which  may  or 
may  not  be  one  of  the  principal  lines  of  the  survey),  the  angles  to  the  various  objects  are 
measured,  and  their  distances  from  the  instrument  are  determined  by  means  of  the  stadia 
"  wires  "  in  the  telescope.  Hence  an  angle  and  a  distance  must  be  laid  off  on  the  drawing 
to  locate  the  observed  points.  The  problem  is  not  essentially  different  from  some  already 
considered,  but  the  desirability  of  speed  in  the  operation  of  plotting  leads  to  different  methods, 
and  this  usually  means  the  use  of  a  special  form  of  protractor. 

The  combination  of  protractor  and  scale  shown  in  Fig.  26  is  the  device  of  Mr.  Clifford 
-Foss  of  Boston  and  has  been  in  satisfactory  use  for  several  years.  It  is  made  from  a  circular 
paper  protractor  and  a  paper  scale,  the  former  being  cut  away  so  that  the  scale  may  be  set  in 
with  its  back  flush  with  the  back  of  the  protractor,  its  zero  of  graduations  at  the  center  of 
the  latter,  and  its  graduated  edge  coincident  with  a  diameter.  The  two  parts  are  fastened 
together  by  pasting  strong  thin  paper  across  their  junction  at  the  back,  and  on  the  front,  so  far 
as  figures  will  allow. 

In  use  the  instrument  is  placed  with  its  center  at  the  point  from  which  the  "side  shots" 
are  to  be  plotted,  and  a  fine  needle  is  thrust  through  the  center  into  the  drawing  board.  The 
whole  is  now  free  to  rotate  about  this  point,  and  to  repeat  the  angles  measured  by  the  transit 
which,  in  the  field  work,  was  set  at  the  point  on  the  ground  now  represented  by  the  position 


38 


PLOTTING 


of  the  needle.     The  figure  shows  the  circle  graduations  numbered  for  reading  azimuths  from 
the  rear  end  of  the  line  upon  which  the  center  of  the  instrument  is  placed,  though  they  may, 
c  of  course,  be  numbered  to  suit  any  other  method  of 

I  making  the  field  observations.      The  whole  instru- 

ment is  rotated  till  the  required  circle  graduation  is 
brought  to  the  line  AB,  then  the  distance  to  the 
object  is  laid  off  at  the  edge  of  the  scale. 

As  the  circle  must  be  cut  away  for  a  few  degrees 
each  side  of  the  point  where  zero  would  otherwise  be 

shown,   angles  falling 

A Hi0  ?~[i  i   i  i   i  i   i  i   i  I   I  I   I  I  I  I   I  II  1  I   I  I  I   I      I      within  this  range  are 

protracted  by  means 
of  an  auxiliary  arc 
shown  at  the  left  of 

the  figure.     The  proper  graduation  on  this  short 
arc  is  brought  to  the  line  BC  which  is  an  extension 
of  AB,  and  is  hidden  in  the  figure  by  the  edge  of 
Q  the  scale. 

Some  prefer  'that  the  zero  of  the  circle  (or  the 

*"  '  180  degree  mark,  as  the  field  method  may  require) 

be  placed  at  point  E  since  the  protractor  readings  will  then  be  directly  before  the  eye.  In 
this  case  a  line  DF  is  drawn  perpendicular  to  the  survey  line  AB,  and  to  it  are  brought  the 
graduations  of  the  protractor.  Two  or  more  schemes  of  numbering  may  be  employed  on  one 


B 

r           c 

~t 

0 

i 

1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 

1        23456        789 

1         1 
44    46    48 

PROBLEMS 


39 


protractor,  though  usually  but  one  method  of  field  work  will  be  followed,  and  the  protractor 
will  be  made  to  correspond  to  it. 

The  leading  desirable  features  of  this  form  of  instrument  are  :  first,  that  the  protractor 
and  scale  are  in  one  piece  ;  second  (and  more  important),  that  practically  the  whole  length  of 
the  scale  is  available.  The  first-named  feature  renders  it  necessary  to  have  several  complete 
instruments  with  different  scales  for  the  lineal  measurements. 

46.  Problems.  In  most  cases  where  exercises  and  problems  involve  the  plotting  of 
angles  it  is  advisable  to  draw  the  outline  on  paper  of  generous  dimensions,  since  the  opera- 
tions of  plotting  extend  considerably  beyond  the  finished  boundaries.  This  paper  should 
be  smooth  and  firm,  but  not  necessarily  of  a  quality  required  for  good  inked  work.  The 
finished  plot  may  be  transferred  by  pricking  (Art.  142)  to  the  final  sheet,  and  the  drawing 
finished. 

1.     The  following  problems  in  finished  form  may  be  placed  on  sheets  11  x  15  inches  :  — 


LENGTH  OF 
COURSE,  FEET 

DEFLECTION 
ANGLE 

METHOD  OF 
PLOTTING 

336.0 
87.5 

76°  -35'  r 
68°  -10'  r 

Protractor  (Art.  36) 
it 

60.0 
201.0 
118.5 

103°  -30'  I 
102°  -20'  r 
47°  -50'  r 

Chord  (Art.  38) 
Tangent  (Art.  37) 
tt 

394.0 

84°  -00'  r 

Chord 

245.7 

84°  -35'  r 

(i 

40 


PLOTTING 


Unless  it  is  known  in  what  direction  the  courses  proceed,  it  is  possible  to  plot  two  differ- 
ent figures  from  notes  like  the  above.  In  this  problem  consider  the  first  course  as  having  a 
bearing  of  N  68°-15'  E. 

(a)  Make  a  free-hand  sketch  of  the  figure,  compute  the  interior  angles,  and  apply  the  test 
given  in  Art.  40. 

(6)  Plot  the  figure  to  a  scale  of  1  inch=  40  feet,  using  the  methods  given  in  the  third 
column  for  plotting  the  angles.  The  free-hand  sketch  should  show  whether  in  any  given  case 
it  is  better  to  plot  the  interior  or  the  deflection  angle. 

2.  Given  the  following  notes  for  a  closed  polygon,  the  azimuths  being  read  from  the 
south  :  — 


LENGTH  OF 
COURSE,  FEET 

AZIMUTH 

852.6 

28°  -30' 

769.7 

136°  -20' 

475.0 

234°  -15' 

249.0 

327°  -45' 

438.5 

253°  -20' 

(a)  Make  a  free-hand  sketch ;  compute  the  bearings  and  interior  angles,  and  write  them 
on  the  sketch  ;  determine  whether  the  sum  of  the  interior  angles  is  correct. 

(5)  Make  a  table  with  the  following  headings,  calculate  the  total  latitudes  and  longitudes, 
and  use  these  to  plot  the  figure  to  a  scale  of  1  inch=  100  feet  (Art.  43).  In  making  the 
table  the  course  leading  from  the  most  westerly  vertex  should  occupy  the  first  line. 


41 


LENGTH  OF 
COURSE,  FEET 

BEARING 

LATITUDE 

LONGITUDE 

TOTAL 
LATITUDE 

TOTAL 
LONGITUDE 

+ 

- 

+ 

- 

3.  On  a  scale  of  1  inch  =  200  feet  lay  down  coordinate  lines  500  feet  apart  from  3500  E 
to  6000  E,  both  inclusive,  and  1000  N  to  2500  N,  both  inclusive. 

The  coordinates  of  A,  the  beginning  of  course  AB,  are  1284  N,  3692  E ;  the  course  is 
1050  feet  long  and  runs  N  62°-50'  E.  Compute  and  plot  the  coordinates  of  B,  and  draw 
AB. 

From  the  following  data  compute  the  coordinates  for,  and  plot  the  three  courses  suc- 
ceeding AB:  — 

BC  is  516.5  feet  long  and  makes  a  deflection  angle  of  53°-10'  to  the  right  of  AB. 

CD  is  754.0  feet  long,  with  azimuth  240°-30'  from  the  south. 

DE  is  630.4  feet  long  and  makes  an  interior  angle  of  76°-10'  with  CD,  the  general 
direction  of  DE  being  northwest. 

Find  also  the  coordinates  for  F,  the  extremity  of  AF  which  passes  through  the  intersec- 
tion of  2000  N  and  4000  E,  and  is  1080  feet  long. 

Draw  FE  and  find  its  length  and  bearing.     . 

A  check  observation  from  the  intersection  of  2000  N  and  5000  E  shows  E  to  be  distant 
482.83  feet,  with  bearing  N  40°-35'  E.  Compare  the  coordinates  of  E  calculated  from  this 
observation  with  those  previously  calculated. 

In  the  above  work  use  the  nearest  hundredth  of  a  foot  in  distances,  and  the  nearest  ten 
seconds  in  arc. 


CHAPTER   IV 


TOPOGRAPHICAL    DRAWING   IN   INK 

47.  Topographical  Symbols  in  General.  The  outlines  of  a  map  having  been  drawn  by 
methods  already  described,  the  surfaces  of  the  various  portions  are  finished  with  appropriate 
symbols  and  markings.  These  give  relief  and  variety  to  the  map  and  convey  at  once  an  idea 
of  the  physical  condition  of  the  surface  —  first,  as  to  the  distribution  of  land  and  water ; 

second,  as  to  the  various  forms  of  vegetation   on  the 

land  surfaces  (or  the  character  of  the  ground  if  no  vege- 
tation is  present);  and  third,  as  to  the  configuration 
of  the  ground.  In  this  last  instance  the  method  of  indi- 
cating relative  heights  of  various  portions  of  the  surface 
is  usually  by  means  of  contour  lines  which  will  be 
considered  in  another  chapter.  These  do  not  give  a 
pictorial  effect.  It  is  sometimes  desirable  to  give  a  defi- 
nite suggestion  of  a  steep  declivity,  as  a  railroad  em- 
bankment or  cut,  or  a  headland,  and  a  special  symbol  is  in  use  for  that  purpose. 

To  suggest  clearly  an  idea  of  the  objects  represented,  symbols  are  to  a  certain  extent 
pictorial.  They  are  sometimes  represented  in  elevation  and  sometimes  in  plan.  Thus  the 
symbol  for  grass  land  (Fig.  29)  is  obviously  a  tuft  of  grass  shown  in  elevation,  while  that 

42 


Fig.  27. 


THE  SIZES  AND  DISTRIBUTION   OF   SYMBOLS 


43 


for  cultivated  land  (Fig.  31)  is  an  attempt  to  suggest  furrows  in  plan.  A  more  general 
pictorial  effect  is  sought  in  some  cases,  as  in  the  representation  of  fresh  marsh.  Compare  Fig  27, 
which  is  from  a  photograph,  with  the  symbol,  Fig.  34;  and  Fig.  28,  which  is  also  from  a 
photograph,  with  the  corre- 
sponding method  of  repre- 
sentation, Fig.  35. 

Indeed,  these  represen- 
tations are  so  pictorial  in 
character  that  the  term  sym- 
bol is  not  very  appropriate, 
but  its  use  has  become  so 
common  as  a  convenient  term 
that  it  is  retained  here. 

From  a  photograph  by  Mr.  William  Lyman  Underwood. 

48.     The  Sizes  and  Dis-  Flgl  28< 

tribution  of  Symbols  is  a  matter  demanding  some  attention,  but  no  fixed  rules  covering  all 
cases  can  be  given.  The  sizes  will  vary  somewhat  with  the  size  and  scale  of  the  map,  but  not 
in  exact  proportion  therewith.  As  soon  as  the  draftsman  has  a  clear  idea  what  his  finished 
map  should  look  like  he  properly  adapts  his  symbols  to  secure  that  appearance.  The  follow- 
ing may  be  stated  as  the  leading  characteristics  of  a  good  map  so  far  as  the  symbols  contribute 
to  its  appearance:  When  viewed  from  the  point  dictated  by  its  size,  scale,  and  purpose,  no 
portion  of  the  surface  should  appear  more  prominent  than  would  the  corresponding  portion 
of  the  actual  earth's  surface  ;  the  individual  symbols  must  not  be  so  large  as  to  be  obtrusive 


.....vU/y... 


a 


44  TOPOGRAPHICAL   DRAWING  IN   INK 

or  to  suggest  that  they  were  drawn  large  in  order  to  cover  the  area  more  quickly,  neither 
should  they  be  so  minute  as  to  seem  affected;  there  must  be  clearness  and  a  definite  purpose 
in  each  stroke,  so  that  every  portion  of  the  map  will  bear  close  inspection. 

49.  Grass  Land,  Fig.  29,  is  indicated  by  covering  the  area  evenly  with  the  symbol,  but 
without  preserving  a  definite  geometrical  order  in  repeating  it.  At  a  it  is  shown  that  the  tuft 

consists  of  an  odd  number  of  strokes,  the  middle  one  standing 
vertical,  while  the  others  are  curved.  The  extreme  strokes  are 
hardly  more  than  dots.  The  general  outline  to  be  kept  in  mind  is 
indicated  at  b.  In  drawing  the  tuft  the  strokes  may  be  made  in 
order  from  left  to  right  or  the  middle  one  may  be  drawn  first  and 
the  others  drawn  on  either  side  of  it,  as  the  draftsman  chooses. 

It  is  essential  that  the  bases  of  the  individual  tufts  shall  be  on 
Fig.  2V.  straight  lines  parallel  to  the  lower  edge  of  the  drawing,  and  that 

there  be  no  suggestion  of  geometrical  arrangement. 

If  difficulty  is  experienced  in  these  particulars,  aid  may  be  secured  by  ruling  parallel  pen- 
cil lines  considerably  nearer  together  than  the  required  average  distance  between  symbols  and 
by  drawing  the  bases  of  the  symbols  to  these  lines.  Whether  or  not  advantage  be  taken  of  this 
assistance,  the  symbols  should  be  placedat  first  in  a  very  scattering  manner,  covering  the  area  with 
them  far  apart  in  all  directions,  and  gradually  bringing  the  whole  to  the  desired  appearance 
by  going  over  the  surface  several  times,  each  time  filling  up  the  most  obviously  open  spaces. 
It  is  best  on  first  going  over  the  area  to  draw  the  symbols  with  seven  strokes,  and  in  the  sub- 
sequent filling-in  to  use  a  fair  sprinkling  of  five-stroke  and  three-stroke  symbols,  the  lat- 


CULTIVATED  LAND 


45 


ter  being  used  where  there  is  only  a  slight  appearance  of  a  blank  space.     Even  single  dots 
may  be  used  at  the  very  last  to  obtain  an  appearance  of  absolutely  even  tint. 

By  placing  the  ruled  pencil  lines  near  together  the  necessity  of  drawing  many  symbols 
on  any  one  line  is  reduced,  and  the  suggestion  of  geometrical  arrangement  is  thus  avoided. 
These  lines  do  not  need  to  be  exactly  equidistant,  and  so  may  be 
ruled  quite  rapidly. 

The  expedient  of  first  covering  the  surface  with  symbols  drawn 
in  a  widely  scattering  manner  should  be  resorted  to  in  all  cases 
where  geometrical  arrangement  is  to  be  avoided. 


Fig.  30. 


50.  Cleared  Land,  Fig.  30,  is  shown  by  the  symbol  for  grass 
with  a  sprinkling  of  bushes  drawn  as  for  trees,  Fig.  33.     The  grass 
tufts  may  be  drawn  slightly  higher  in  proportion  to  their  width  than 
is  the  case  in  showing  grass  land,  thereby  indicating  a  ranker  growth. 

51.  Cultivated  Land,  Fig.  31.     Here  regularity  in  arrangement 
is  desired.     The  alternate  lines  of  short  dashes  and  of  dots  are 
drawn  with  a  ruling  pen  against  a  straight  edge.     The  breaks  be- 
tween dashes  should  be  short  and  uniform,  and  while  the  dashes 
should  be  of  uniform  length,  care  must  be  taken  that  there  may 
not  be  a  series  of  these  breaks  opposite  each  other  in  adjacent  lines, 

thus  suggesting  a  white  line  crossing  the  lines  of  dashes.  The  object  to  be  represented  here  is 
a  series  of  furrows.  Variety  is  obtained  by  assuming  that  the  field  is  broken  up  into  sections, 
with  the  furrows  running  in  different  directions  in  adjacent  sections. 


46 


TOPOGRAPHICAL  DRAWING  IN  INK 


52.  Sand,  Gravel,  and  Mud,  Fig.  32.  In  general,  areas  covered  by  sand  are  represented 
by  fine  dots  distributed  evenly  over  the  surface,  but  without  order.  Sand  hills  or  dunes  are 
represented  by  leaving  blank  spaces  for  summits  or  ridges.  When  one  edge  of  an  area  is 
sharply  limited,  as  by  a  shore  line  for  instance,  the  dots  are  placed  in  order  for  some  distance 

back  from  the  limiting  line.  A  row  of  somewhat  heavy  dots  is  first 
placed  close  to  and  parallel  with  the  line,  and  the  dots  in  the  second 
row  are  so  placed  that  each  one  is  the  vertex  of  an  equilateral  tri- 
angle, its  two  nearest  neighbors  in  the  first  row  being  the  other 
two  vertices.  As  the  work  proceeds  away  from  the  edge  the  dots 
are  made  finer  and  the  sizes  of  the  triangles  are  increased,  thus 
giving  the  appearance  of  a  graded  gray  tint  which  grows  lighter  as 
it  recedes  from  the  defining  edge.  This  work  must  be  done  with 


Mud. 


Fig.  32. 


some  deliberation,  especially  where  the  dots  are  arranged  in  order;  even  where  they  are  not 
so  arranged  the  pen  must  be  brought  squarely  down  upon  the  paper,  and  must  be  raised  from 
it  without  having  been  pushed  along  the  paper  in  any  direction,  in  order  that  a  perfectly 
round  dot  may  be  produced. 

Gravel  is  represented  by  the  symbol  for  sand,  with  a  mixture  of  small  closed  curved  figures 
and  a  few  angular  figures  representing  stones.  The  dots  may  be  coarser  and  more 
irregular  in  size  than  in  the  representation  of  sand. 

Mud  is  shown  by  sets  of  short  dashes  drawn  free-hand  parallel  to  the  base  of  the  sheet. 
The  edges  of  adjacent  sets  may  be  separated  very  slightly,  thus  giving  an  appearance  of  a  dark 
gray  color  intersected  irregularly  by  fine  white  lines.  The  area  should  first  be  covered  by 
scattered  groups  of  dashes,  and  the  blank  spaces  should  then  be  gradually  filled. 


TEEES 


Evergreen. 


53.  Trees,  Fig.  33.  The  symbol  for  deciduous  trees  must  be  drawn  with  great  care. 
The  usual  tendency  is  to  introduce  too  many  strokes  in  the  vain  hope  of  bringing  out  a  picture 
of  a  well-rounded  tree,  whereas,  the  appearance  of  light,  loose  texture,  characteristic  of  trees 
seen  in  plan,  is  desired. 

This  is  the  first  symbol  in  which  it  is  necessary  to  consider  illumination.  The  upper  left-hand 
half  of  each  tree  is  supposed  to  be  in  sunlight.  The  lower  right-hand  side  will  then  be  in  shade, 
and  on  that  side  the  shadow  of  the  tree  will  fall.  On  the  illuminated  side  mere  outlines  sugges- 
tive of  two  or  three  main  branches  should  be  shown  in  fine  lines,  while 
on  the  opposite  side  the  strokes  should  be  heavier  and  more  numerous. 
The  long  axis  of  the  elliptical  shadow  should  lie  at  45°  with  a  hori- 
zontal line,  and  the  free-hand  lines  of  which  the  shadow  is  composed 
must  be  at  right  angles  to  this  axis.  The  draftsman  may  find  it  nec- 
essary at  first  to  draw  the  outline  of  the  shadow  in  pencil.  If  difficulty 
is  experienced  in  drawing  this  sign,  it  may  be  traced  several  times 
from  the  figure  till  the  relations  and  forms  of  the  outlines  are  learned. 

Individual  Evergreen  Trees  are  not  so  commonly  represented  as 
are  those  of  the  deciduous  sort.  The  white  area  in  the  center, 
shown  in  Fig.  33,  should  first  be  provided  for  by  drawing  a  circle 
in  pencil  from  which  the  spray -like  limbs  radiate.  The  shadow,  as 
shown,  is  tapered  to  suggest  a  cone-shaped  tree. 


Fig.  33. 

54.     Foliage  in  Mass,  Fig.   34.     In  drawing  this  symbol  there  is   often  a   tendency  to 
cover  the  paper  too  thickly,  and  to  make  aimless  strokes.     The  symbol  for  individual  trees 


48 


TOPOGRAPHICAL   DRAWING   IN   INK 


- 

General  Deciduous  Growth. 


Oak  Evergreen 


Fig.  34. 


Fig.  35. 


is  the  basis  to  be  kept  in  mind,  but  for  growth  in  mass  a  more 
sketchy  treatment  is  desirable.  The  area  should  not  be  covered 
uniformly,  but  by  suggestions  of  irregular  groups  of  trees.  See 
also  Fig.  27. 

Fig.  84  also  shows  a  special  sign  for  oak,  and  two  symbols  for 
evergreen,  both  of  which  may  be  used  on  the  same  area. 

Considerable  practice  may  be  needed  in  this  work,  especially 
in  showing  deciduous  growth. 

55.  Fresh  Marsh,  Fig.  35.  The  representation  is  of  irregular 
patches  of  ground  rising  slightly  above  shallow  water,  and  covered 
with  rank  grass.  A  few  tufts  of  grass  in  the  water  itself  give 
the  idea  of  shallowness. 

The  outlines  of  the  land  should  first  be  drawn  in  pencil,  after 
which  the  lines  representing  the  water  should  be  ruled  parallel  to 
the  lower  edge  of  the  drawing.  These  must  be  rather  close  to- 
gether, otherwise  they  will  not  serve  well  to  outline  the  land  areas. 
On  the  lower  side  of  each  island  short  inter-linings  are  drawn  free- 
hand and  very  fine.  They  suggest  a  reflection  of  the  island,  and 
therefore  give  an  appearance  of  relief  ;  they  also  serve  to  outline 
the  indentations  of  the  islands  more  accurately  than  would  other- 
wise be  possible.  The  tufts  of  grass  and  a  few  small  bushes  com- 
plete the  representation. 


WATER 


49 


56.  Salt  Marsh,  Fig.  36.     The  ruled  lines   may   be   farther 
apart  than  in  the  symbol  for  fresh  marsh,  since  there  are  no  islands 
to  be  defined. 

57.  Water,    Fig.    37.      No   feature   of   a   topographical   plan 
adds  more  to  its  good  appearance  than  the  skillful  representation  of 
a  body  of  water. 

The  shore  line  is  first  drawn,  free-hand,  as  a  firm  heavy  line. 
A  coarse  pen  should  be  used  so  that  no  pressure  will  be  required 
to  produce  a  line  of  the  required  weight.  The  first  "  water  line  " 
is  then  drawn  as  close  to  the  shore  line  as  the  skill  of  the  drafts- 
man permits.  The  eye  should  be  kept  on  the  spaces  between  the 
lines  rather  than  on  the  lines  themselves.  Successive  water  lines 
are  then  drawn  at  constantly  increasing  distances.  As  the  work 
progresses,  the  lines  are  made  finer  by  the  use  of  successively  finer 
pens. 

Three  Essentials  are  to  be  noted  :  - 

First,  the  water  lines  must  be  wavy  in  form,  this  effect  being 
secured  by  making  the  lines  a  succession  of  curves  concave  toward 
the  shore.  The  indentations  of  the  shore  will  often  dictate  the 
points  where  two  such  curved  lines  join,  but  the  curved  form  must 
be  maintained  even  where  a  long  smooth  stretch  of  shore  line 
occurs.  In  every  instance  the  wavy  form  must  be  worked  in  very 


Fig.  36. 


Fig.  37. 


50  TOPOGRAPHICAL  DRAWING  IK  INK 

gradually,  the  first  two  or  three  lines  following  the  shore  line  without  a  hint  of  wave 
except  as  the  form  of  the  shore  may  incidentally  produce  it.  The  junctions  of  curves  are  con- 
venient points  for  lifting  the  pen  and  changing  the  position  of  the  hand ;  but  there  must  be  no 
indication  that  the  line  was  stopped  at  such  a  point,  neither  should  there  be  a  slight  open 
space  between  the  ends  of  the  lines,  nor  a  crossing  of  the  ends,  nor  a  thickening  of  the  line  at 
the  junction. 

Second,  the  points  at  which  the  curves  join  must  not  be  chosen  at  random,  but  must  be 
opposite  each  other  in  successive  water  lines.  To  insure  this  arrangement  pencil  lines  should 
be  drawn  normal  to  the  shore  line  at  each  place  where  a  row  of  these  junction  points  will  oc- 
cur, as  at  a,  Fig.  37.  This  pencil  guide-line  is  especially  useful  in  the  long  stretches  where 
there  are  no  indentations  in  the  shore  line. 

Third,  two  adjacent  water  lines  must  be  equidistant  throughout  their  extent.  As  a  step 
toward  this  end,  at  the  same  time  providing  for  spacing  the  lines  at  successively  greater  dis- 
tances, a  row  of  dots  should  be  drawn  normal  to  the  shore  line,  as  at  5,  the  distance  between 
them  being  gradually  increased  as  they  recede  from  the  shore  line.  The  edge  of  a  piece  of 
paper  may  now  be  placed  alongside  the  dots,  and  their  relative  positions  copied  on  the  strip. 
This  should  then  be  placed  at  intervals  normal  to  the  shore  line,  and  the  positions  of  the  dots 
copied  on  the  drawing,  where  they  will  serve  as  a  gauge  for  properly  spacing  the  water  lines. 

Having  begun  any  given  water  line  it  must  be  finished  before  another  is  commenced. 
The  paper  should  be  shifted  frequently  (or  the  body  shifted  relative  to  the  drawing,  if  the 
latter  is  large)  so  that  the  hand  and  arm  will  not  be  in  a  cramped  position  as  the  lines  are 
drawn.  In  general  draftsmen  draw  most  steadily  when  the  strokes  are  made  downward 
toward  the  body. 


51 


If  the  body  of  water  is  small,  the  water  lining  may  cover  the 
entire  area  ;  if  it  is  quite  large,  only  a  few  lines  at  the  edge  need 
be  drawn. 

58.  Roads  and  Streets,  Fig.  38.  The  method  of  drawing 
highways  and  streets  with  sidewalks  apparently  violates  the  general 
rule  for  the  use  of  shade  lines,  since  these  are  shown  at  the  left- 
hand  and  upper  street  lines.  The  assumption  is  that  the  land  at 
the  sides  of  the  streets  is  at  a  higher  elevation  than  the  road  bed, 
and  the  various  parcels  of  land  are  the  objects  whose  boundaries  are 

considered  relative  to  shading  ;  hence 
the  heavy  lines  should  be  considered  as 
the  right-hand  and  lower  sides  of  the 
lots  of  land  adjacent  to  the  streets. 


..HllUlilll 


Embankment 


Cut 


..Foot  Path 
-Cart  Path 

I  Rough  Road 


.Highway 

Street  with 
sidewalks 


i  i  i  i  i  i  i  i 


-H+l-trackR.R. 

:cx2-trackR.R. 
.Street 
•Railway 


Fig.  38. 


Fig.  39. 


59.  Railways  also  are  shown  in  Fig.  38,  and  need  no  comment. 

60.  Embankments  and  Cuts,  Fig.  39.     Steep  declivities,  such 
as  occur  on  headlands  eroded  by  the  action  of  water,  or  such  as  are 
formed  artificially  at  railway  embankments  and  cuts,  are  indicated 
by  series  of  tapered  lines  or  "hachures."      The  flat  top  of  an  em- 
bankment, or  the  bottom  of  a  cut,  is  shown  by  a  blank  area  of  the 
appropriate  width  between  the  series  of  tapered  lines. 

In  the  embankment  the  thick  ends  of  the  hachures  are  at  the 
flat  top  of  the  embankment,  while  in  the  cut  the  thin  ends  are  at 


52 


TOPOGRAPHICAL  DRAWING   IN   INK 


Ledge 


Fence 
Rough  Wall 
Face  Wall 
Hedge 


the  flat  bottom;  that  is,  in  each  case  the  thin  ends  point  down  the 
slope. 

The  slopes  are  represented  by  single  strokes  with  a  fine,  flexible 
pen  (such  as  Gillott's  mapping  pen)  when  the  area  to  be  covered  is 
not  too  wide  to  accommodate  a  free  movement  of  the  fingers.  A 
skilled  draftsman  practiced  in  this  work  will  draw  hachures  an  inch 
long  with  single,  quick  strokes ;  in  general,  however,  if  the  area  is 
more  than  three  eighths  to  one  half  inch  wide,  it  is  necessary 
to  proceed  as  shown  in  the  second  representation  of  embankment, 
Fig.  39.  (The  same  method  is  applicable  to  representing  a  cut.) 
The  area  is  divided  into  longitudinal  strips,  each  of  which  is  filled 
with  hachures  which  do  not  taper ;  but  which,  in  successive  strips, 
are  graded  as  to  weight  and  spacing,  so  that  the  result  resembles 
that  of  single  long  strokes. 

61.  Ledge,  Fig.  40.  The  area  to  be  covered  should  first  be  roughly  blocked  out  in  pencil, 
as  shown  at  a.     Each  small  area  thus  formed  should  then  be  covered  by  a  series  of  very  fine 
parallel  lines,  drawn  free-hand,  as  shown  at  b.     Seams  and  crevices  are  then  worked  in. 

62.  Fence,  Wall,  and  Hedge.     Fig.  40  shows  also  the  signs  used  for  these  features. 

_j     L.     rJZ^in     vJZfoT*  63.     Buildings.     In  some  cases  it  is  not  a  matter  of  interest  to  show 

V,///'//\         V/////YA 

| 1     vsfa/rt     VW///A      the  material  of  which  buildings  are  constructed  ;  in  this  case  they  are 

drawn  either  as  shown  for  wood  or  for  stone,  Fig.  41.     If  it  is  desired 
Fig.  41 .  to  indicate  the  material  the  method  shown  in  the  figure  may  be  used. 


Fig.  40. 


1 

Grass        Cleared 
Land           Land 
(49)            (50) 

r  ,        ,    Sand  (52) 
Cultivafed  

Land     Gravel   (52) 
*-lJ"—  *  Mud  (52) 

Trees  (Orchard)  (53) 

/v 

t-+ 

\  r 

,"* 

Deciduous   Evergreen 
Foliage      Foliage 
(54)         (54) 

i 

Fresh       Salt 
Marsh     Marsh 

(55)          (56} 

Water  (57) 

Roads  and  Streets 

(58) 

Railways    (59) 

1st  method  1st  method 

2d  method  ?d  method 

Embank-       Cut 
ment(60)      (60) 

fence,  Walls, 

•Hedge  (6Z) 
Ledge(6l)  | 

'Buildings 
!     (63)y 

I 

Plate  I. 

53 


Plate  II. 

65 


EXEECISES  57 

64.  Exercises.  1.  Plate  I  shows  the  lay-out  of  a  sheet  with  border  line  10  x  14  inches, 
for  practice  in  making  the  various  topographical  signs.  The  sheet  is  first  divided  into  nine 
equal  rectangles  as  shown  by  the  broken  lines.  Each  rectangle  is  then  furnished  with  a 
border  line  |-  inch  from  its  edges,  and  is  filled  with  the  sign  or  signs  indicated.  The  figures 
in  parentheses  refer  to  the  sections  which  describe  the  various  signs. 

For  this  work  paper  with  a  smooth,  hard  surface  is  best,  such  as  linen  record  paper,  01 
Bristol  or  Strathmore  board  ;  tracing  cloth  is  also  suitable. 

It  frequently  happens  that  s,ome  symbols  will  not  be  satisfactorily  executed,  and  a 
student's  time  will  not  permit  that  the  whole  sheet  be  repeated  till  all  portions  are  satisfac- 
tory. It  is  suggested  that  the  nine  rectangles  be  considered  separately,  and  that  they  be 
cut  out  on  the  broken  lines.  Any  one  of  these  may  then  be  repeated  without  sacrificing  the 
others,  and  when  all  are  completed,  they  may  be  kept  as  separate  cards  or  mounted  in 
order  on  a  large  sheet. 

2.  Plate  II  shows  the  topographical  symbols  used  in  a  map.  This  may  be  enlarged  to 
10  x  14  inches  by  any  method  explained  in  Chapter  VIII,  and  drawn  as  an  exercise  in  the 
use  of  symbols. 


CHAPTER  V 

TOPOGRAPHICAL    DRAWING   IN   COLORS 

65.  Preparation  of  the  Color.     One  of  the  cabinet  saucers  is  first  filled  about  half  full 
from  the  water  glass.     A  clean  brush  dipped  in  clean  water  is  then  pressed  against  the  rim 
of  the  glass  to  remove  a  considerable  portion  of  the  water  which  it  will  have  taken  up.     The 
brush  is  then  dabbled  first  in  the  pan  of  color,  then  in  the  saucer  of  water,  and  so  continued 
until  the  water  has  acquired  the  required  depth  of  color,  which  is  determined  by  applying  a 
brushful  to  a  bit  of  paper  of  the  same  kind  as  that  on  which  the  color  is  to  be  used. 

With  light,  transparent  colors,  such  as  gamboge,  this  is  the  end  of  the  process  ;  with 
heavy  colors,  such  as  burnt  sienna,  the  preparation  must  be  allowed  to  stand  quietly  for  a 
few  moments  to  settle.  It  is  then  quickly  poured  into  another  saucer,  care  being  taken  that 
the  settlings  be  retained  in  the  first  saucer. 

66.  The  Nature  of  a  Tint.     The  color  prepared  as  directed  above  should  not  be  regarded 
as  paint,  a  coating  of  which  is  to  be  spread  thickly  over  the  paper,  but  rather  as  water  slightly 
colored,  a  thin  film  of  which  is  to  be  evenly  and  lightly  applied.     If  the  paper  could  be 
dipped  into  this  water  and  held  up  by  one  edge  so  that  all  surplus  water  would  run  off,  the 
proper  effect  of  tinted  paper  would  be  secured.     But  as  this  is  not  practicable  in  making 
drawings,  a  brush  is  used  to  spread  the  color  over  the  desired  areas.     Water  colors  are  more 

68 


APPLYING  THE  COLOR  59 

or  less  transparent  when  thinly  applied,  and  the  white  of  the  paper  beneath  the  color  modi- 
fies it  so  that  what  might  otherwise  be  a  crude  glaring  effect  is  toned  to  a  pleasing  tint. 

67.  Applying  the  Color.  The  board  upon  which  the  paper  has  been  stretched  (Art.  29) 
should  be  raised  at  its  back  edge  so  that  the  surface  will  slope  downward  toward  the  drafts- 
man, making  an  angle  of  about  20°  with  the  horizontal. 

With  the  brush  charged  with  color,  but  not  filled  as  full  as  it  will  hold,  begin  at  the 
upper  left-hand  corner  of  the  area  to  be  colored,  and  draw  a  band  from  left  to  right  as  broad 
as  the  brush  will  lay  smoothly.  Cause  the  point  of  the  brush  to  travel  along  the  upper 
boundary  so  that  it  will  not  be  necessary  to  go  over  the  ground  again.  The  surplus  color 
will  at  once  run  to  the  lower  edge  of  the  band.  Having  worked  the  tint  exactly  up  to  the  right- 
hand  boundary,  draw  another  band  from  right  to  left  joining  the  first  one.  The  surplus 
color  will  all  run  to  the  bottom  of  the  second  band,  and  if  the  work  is  done  quickly,  so  that 
the  lower  edge  of  the  first  band  has  not  begun  to  dry,  the  two  bands  will  be  perfectly  blended 
together  into  a  single  broad  one.  This  process  is  repeated  till  the  whole  area  is  covered, 
when  the  remaining  surplus  color  is  taken  up  with  blotting  paper,  or  with  the  brush  dried  by 
touching  it  to  blotting  paper.  When  dry,  the  color  should  be  perfectly  "  flat,"  that  is,  of 
uniform  depth,  without  spots  or  streaks. 

In  general  the  desired  tint  is  secured  by  a  single  wash  of  color,  but  some  colors,  such  as 
Prussian  blue,  are  difficult  to  lay  flat,  and  it  is  better  to  lay  two  weak  washes,  giving  the 
first  ample  time  to  dry  before  the  second  is  applied. 

The  following  general  directions  must  be  followed  to  attain  success  :  — 

1.   The  brush  must  not  be  regarded  as  a  pen  or  pencil  whose  point  only  is  to  be  used  ;  on 


60  TOPOGRAPHICAL  DRAWING  IN   COLORS 

the  contrary  it  is  an  instrument  for  spreading  the  color  in  broad  areas,  and  to  this  end  it  is 
pressed  against  the  paper  so  that  practically  the  whole  side  is  in  contact  with  it. 

2.  The  brush  must  be  filled  often,  but  never  so  full  as  it  will  carry. 

3.  The  work  must  progress  so  rapidly  that  no  band  of  color  will  have  dried,  or  even 
"  set "  at  its  lower  edge  before  the  next  one  is  joined   to   it.     In   fact   the   brush   must  be 
considerably  in  advance  of  the  nearest  point  where  the  color  has  dried,  otherwise  streaks  and 
blotches  will  result. 

Speed  is  not  gained  by  hurried  nervous  strokes.  The  sweep  of  the  brush  may  be 
deliberate,  even  slow,  but  it  must  cover  a  wide  band,  and  cover  it  thoroughly,  so  that  it  will 
not  be  necessary  to  go  back  to  touch  up  blank  spots.  The  wash  must  also  be  carried  fully 
out  to  the  boundaries  as  the  work  progresses.  It  is  fatal  to  go  over  the  surface  the  second 
time  when  the  first  wash  has  made  the  least  beginning  at  drying,  except  as  described  above 
for  two  coats  over  the  entire  area. 

4.  Paper  suited  to  the  work  must  be  used.     (See  Art.  17.) 

5.  Perfect  cleanliness  and  neatness  must  be  observed.     Preliminary  penciling  should  be 
carefully  done  so  as  to  avoid  the  necessity  of  making  erasures.     If  erasures  are  necessary, 
they  should  be  made  with  a  very  soft  rubber,  for  if  the  surface  of  the  paper  be  roughened,  the 
color  will  settle  in  a  darker  tint  than  appears  where  no  erasures  have  been  made. 

A  piece  of  clean  cloth  or  paper  should  be  placed  between  the  hand  and  the  drawing  dur- 
ing  all  stages  of  the  work,  to  protect  the  drawing  from  perspiration,  otherwise  the  color  will 
not  be  flat.  If  from  this  or  any  other  cause  the  paper  is  greasy,  it  should  be  rubbed  lightly 
with  chalk  dust  applied  with  a  soft  cloth  or  chamois  skin.  The  chalk  must  be  thoroughly 
removed,  however,  before  any  color  is  laid  on.  A  little  ox  gall  in  the  color  will  cause  it  to  be 


INKING  61 

worked  more  evenly  on  a  slightly  greasy  surface.  The  point  to  be  attained  is  to  keep  the 
drawing  so  clean  that  none  of  these  expedients  will  be  necessary. 

A  brush  charged  with  one  color  must  be  cleaned  before  touching  it  to  another,  for  each 
color  should  be  kept  free  from  dust,  dirt,  and  stains  of  other  colors. 

As  soon  as  practicable  after  using  a  brush  it  should  be  rinsed  thoroughly  in  clean  water, 
special  care  being  taken  to  get  all  color  out  of  the  heel,  by  pressing  it  repeatedly  against  the 
bottom  or  side  of  the  glass.  It  is  better  not  to  touch  the  hairs  of  the  brush  with  the  fingers. 
When  the  cleaning  is  finished,  hold  the  brush  by  the  end  of  the  handle  and  shake  it  quickly  so 
that  the  water  will  fly  out.  This  should  leave  the  brush  end  straight  and  nicely  pointed, 
as  it  should  always  be  before  it  is  put  away. 

6.  The  color  in  the  saucer  should  frequently  be  stirred  with  the  brush  to  keep  the 
tint  uniform. 

When  large  areas  are  to  be  colored,  the  paper  should  be  slightly,  but  thoroughly  and 
evenly,  moistened  with  a  large  brush  or  soft  sponge.  If  the  color  is  then  applied  before 
the  paper  is  thoroughly  dry,  a  tint  can  be  laid  much  more  rapidly  and  evenly  than  upon  dry 
paper.  When  there  is  much  moisture  in  the  atmosphere,  the  paper  will  absorb  enough  to 
make  a  noticeable  difference  in  its  readiness  to  take  color. 

68.  Inking.  It  is  better  to  defer  the  inking  of  the  drawing  until  after  the  coloring  is 
finished.  This  is  sometimes  inconvenient,  especially  when  there  is  but  little  coloring  as  com- 
pared with  the  amount  of  lining.  If  the  inking  is  done  first,  it  must  be  done  with  waterproof 
ink.  The  main  reasons  for  doing  the  lining  last  are  :  first,  uniformity  of  tint  is  more  easily 
secured ;  and  second,  the  drawing  will  look  more  brilliant  and  clean  cut,  since  the  uniform 


62  TOPOGRAPHICAL  DRAWING  IN  COLORS 

blackness  of  the  lines  will  not  be  injured  by  being  partly  covered  in  places  by  the  color,  as 
would  otherwise  be  the  case.  There  is  a  repellent  quality  in  many  waterproof  inks  that 
results  in  the  color  being  driven  away  from  the  line,  so  that  a  narrow  band  of  the  tinted  area 
adjacent  to  each  inked  line  is  slightly  lighter  than  the  rest. 

69.  Making  Corrections.     If  for  any  cause  portions  of  a  tinted  area  are  darker  than 
others,  the  surplus  color  may  be  removed  by  going  over  the  area  with  a  brush  charged  with 
clean  water,  and  immediately  applying  a  piece  of  clean  blotting  paper.     The  operation  may 
need  several  repetitions.     Another  method,  usually  more  satisfactory,  is  to  rub  the  dark  areas 
gently  with  a  rather  soft  eraser. 

A  light  area  may  be  deepened  in  tone  by  stippling,  a  process  which  consists  in  covering 
the  area  with  small  dots  of  color  applied  with  the  point  of  a  small  brush  or  with  a  pen.  The 
color  should  be  the  same  as  that  used  for  the  wash,  and  individual  dots  should  not  appear  as 
such,  except  upon  very  close  inspection. 

70.  Laying  a  Graded  Tint.     It  is  difficult  to  show  by  a  printed  figure,  either  in  black  or 
in  color,  the  effect  of  a  uniformly  varying  tint.     Fig.  42  is  given  as  an  attempt  to  indicate 
this  effect.     However,  the  following  directions  should  be  sufficient  to  enable  one  to  lay  a 
graded  tint  successfully.     Exercises  in  covering  rectangular  outlines  with  such  a  tint  look 
best  with  the  dark  portion  at  the  top,  as  shown,  but  the  process  should  be  that  of  working 
from  light  to  dark,  the  board  being  turned  so  that  the  edge  which  is  to  be  light  is  at  the  top. 

Provide  two  saucers,  in  one  of  which  is  an  ample  quantity  of  the  color  to  be  used,  mixed 
considerably  darker  than  is  desired  for  the  dark  edge  of  the  area  to  be  colored  ;  in  the  other 
should  be  a  small  quantity  of  clear  water  or  of  weak  tint,  according  to  whether  the  light  edge 


LAYING  A  GRADED   TINT 


63 


of  the  rectangle  is  to  be  colorless  or  to  have  a  slight  color. 
With  the  brush  charged  with  only  a  small  quantity  of  the 
water  or  weak  color  draw  a  band  across  the  top  of  the  rec- 
tangle. Then  take  up  with  the  brush  a  small  quantity  of  the 
strong  color,  mix  it  quickly  but  thoroughly  with  the  contents 
of  the  saucer  first  used,  and  apply  a  second  band  of  this 
slightly  deepened  color  immediately  below  and  touching  the 
first  band,  which  must  not  have  been  allowed  to  dry  before 
the  second  band  is  applied.  The  two  bands  will  blend  to- 
gether. Again  add  some  of  the  strong  color  to  the  weak, 
and  draw  the  third  band,  blending  it  with  the  second. 

The  two  important  points  to  be  observed  are  :  first,  the 
amount  of  color  in  the  brush  when  a  band  is  drawn  must 
not  be  so  great  that  any  considerable  amount  of  excess  liquid 
will  run  to  the  lower  edge  of  the  band,  otherwise  it  will  not 
blend  well  with  the  succeeding  band  ;  second,  a  regularly 


Fig.  42. 


increasing  quantity  of  the  stronger  color  must  be  added  to  the  weaker.  The  additions  are 
in  a  sort  of  geometrical  proportion,  as  the  amount  of  liquid  as  well  as  the  depth  of  color  is 
ever  increasing  in  the  saucer  to  which  the  strong  color  is  added. 

71.  Blending.  The  effect  of  a  blended  edge  of  a  band  of  color  is  the  same  as  that  of  a  graded 
tint;  that  is,  the  color  gradually  fades  away  into  the  white  of  the  paper.  But  the  method  em- 
ployed confines  the  width  of  the  area  in  which  this  grading  takes  place  to  a  single  brush  stroke. 


64  TOPOGEAPHICAL  DRAWING   IN  COLORS 

For  this  work  a  double-end  brush  is  most  convenient,  one  end  being  filled  with  the  color 
to  be  used,  the  other  with  water.  Having  drawn  the  band  of  color,  the  water  brush  is  then 
passed  along  the  edge  to  be  blended,  sufficient  pressure  being  applied  to  spread  the  brush  con- 
siderably. Its  edge  should  just  touch  the  color,  which  will  then  run  into  the  water  band  and 
thus  become  blended.  The  whole  operation  must  be  finished  quickly,  before  the  edge  of  the 
color  band  can  "  set."  In  drawing  the  water  band'  care  must  be  taken  that  the  whole  of  the 
paper  in  the  width  covered  shall  be  wet,  and  that  every  point  in  the  edge  of  the  color  is 
touched.  Only  one  passage  of  the  water  brush  should  be  made,  and  any  attempt  to  remedy 
defective  spots  before  the  whole  work  is  dry  is  sure  to  be  unsuccessful. 

It  is  important  that  neither  brush  be  very  fully  charged.  As  in  laying  a  graded  tint, 
the  color  band  must  not  have  a  puddle  at  its  lower  edge,  and  if  the  water  brush  is  too  heavily 

charged,  the  water  band  will  run  into  the  color, 
whereas  the  color  should  blend  into  the  water. 
If  the  band  is  more  than  about  3  inches 
long,  as  is  frequently  the  case  in  shore  lines, 
for  instance,  the  blending  must  be  started  be- 
'*»"        "  fore  the  color  band  is  finished.     As  shown  in 

Fig.  43,  about  3  inches  of  the  color  band  is  drawn,  then  all  but  about  |-  inch  of  this  is  blended. 
The  color  and  water  bands  are  thus  alternately  applied,  the  latter  always  being  stopped  short 
of  the  end  of  the  former  till  the  last  section  of  the  work  is  reached. 

72.  Mottling,  Fig.  44.  Mottling  consists  in  introducing  spots  and  streaks  of  one  color 
into  a  groundwork  of  another  color,  the  two  being  blended  together.  The  purpose  is  to  re- 


MOTTLING 


65 


lieve  the  monotony  of  a  large  area  of  the  ground  color,  and 
also  to  serve  as  a  topographical  sign.  (See  Art.  79.) 

The  two  colors  should  be  of  equal  strength,  so  that  the 
spots  will  not  stand  out  aggressively;  and,  as  in  all  opera- 
tions involving  blending,  the  brushes  must  be  about  equally, 
and  not  excessively,  charged  with  the  colors. 

Having  laid  a  portion  of  the  ground  color,  put  on  an 
irregular  spot  or  streak  of  the  other  color,  its  upper  edge 
being  brushed  in  contact  with  the  lower  edge  of  the  ground 
color,  where  blending  will  at  once  take  place ;  then  resuming 
the  ground-color  brush,  draw  around  the  spot,  always  touch- 
ing its  edge,  and  continue  the  ground  color  till  it  is  desired 
to  introduce  another  spot.  At  the  lower  edge  of  the  figure 
is  shown  a  spot  as  it  is  brushed  on,  and  before  the  ground 
color  is  brushed  around  it. 

Though  all  this  work  must  be  done  rapidly,  so  that  no 


Fig.  44. 


edge  will  dry  till  the  whole  is  finished,  it  must  be  remembered  that  in  this,  as  in  most  opera- 
tions in  coloring,  rapidity  is  secured  by  using  a  good  sized  brush,  by  putting  sufficient  pres- 
sure upon  it  to  spread  it  well,  and  by  covering  the  paper  completely  the  first  time  the  brush  is 
passed  over  it. 

73.     Dragging,  Fig.  45.     In  this  operation  the  color  is  applied  in  ragged,  cloudlike  patches. 
Dragging  is  used  in  the  representation  of  salt  marsh  (Art.  86)  and  of  rocky  surfaces  (Art.  91). 


66 


TOPOGRAPHICAL   DRAWING   IK   COLORS 


The  brush  must  contain  but  very  little  color.  After  having  dipped  it  into  the  color 
saucer  it  should  be  drawn  across  the  edge  of  the  latter  to  discharge  most  of  the  liquid,  and 

it  may  sometimes  be  necessary  to  further  discharge  it  by 
pressing  the  brush  flatwise  upon  blotting  paper.  If  the 
brush  has  a  ragged  edge  upon  leaving  the  blotting  paper,  so 
much  the  better.  Much  depends  upon  the  shape  of  the 
brush  and  the  amount  of  color  it  contains. 

The  brush  is  held  nearly  flat  upon  the  paper,  and  moved 
always  parallel  with  the  lower  edge  of  the  drawing,  with 
the  handle  in  a  vertical  plane  perpendicular  to  the  direction 
of  motion.  The  pressure  upon  the  paper  should  be  uneven, 
so  that  varying  portions  of  the  brush  will  be  in  contact  from 
moment  to  moment. 

74.     Matching  a  Color.     It  is  often  necessary  to  prepare 
a  color  which  shall  be  exactly  like  one  already  applied  to  a 
drawing.     This  often  proves  surprisingly  difficult  to  do,  as 
Fig.  45.  ^  presence  Of  other  colors  on  the  drawing  deceives  the  eye 

as  to  the  quality  and  intensity  of  the  color  in  question. 

To  eliminate  these  effects  take  a  piece  of  paper  like  that  on  which  the  drawing  is  made, 
cut  a  hole  in  it  at  a  considerable  distance  from  the  edge,  and  apply  a  wash  of  the  trial  color 
around  the  hole,  and  to  a  considerable  distance  from  it.  When  this  color  is  dry,  lay  the  paper 
over  the  drawing  so  that  the  color  to  be  matched  will  show  through  the  hole.  Any  differ- 


COMBINATIONS   OF  COLORS 


67 


ences  between  the  two  washes  will  then  be  clearly  apparent,  and  other  trials  are  made  in  the 
same  manner  till  no  difference  appears. 

75.  Combinations  of  Colors.  While  pigments  for  water  coloring  are  made  in  great 
variety,  it  is  necessary,  in  technical  drawing,  to  have  only  a  few  of  these,  the  remaining  neces- 
sary ones  being  obtained  by  combinations. 

The  pigments  needed  for  the  present  purpose  are  mentioned  in  Art.  22,  and  the  initials 
of-  their  names  as  there  given  will  be  used  in  the  following  pages. 

Starting  with  the  primary  colors  red,  blue,  and  yellow,  the  secondary  and  tertiary  colors 
may  be  derived  as  shown  :  — 


PRIMARIES 

SECONDARIES 

TERTIARIES 

Red 
Blue 
Yellow 

Violet  =  Red  +  Blue 
Green  =  Blue  +  Yellow 
Orange  =  Red  +  Yellow 

Russet  =  Violet  +  Orange 
Citrine  =  Orange  +  Green 
Olive  =  Violet  +  Green 

The  secondaries  are  produced  by  a  combination  of  the  proper  primaries  in  almost  any  pro- 
portion ;  thus  the  addition  of  very  little  yellow  to  blue  will  produce  green,  and  upon  successive 
additions  of  yellow  the  combination  still  remains  green,  though  it  may  pass  through  all  the 
shades  from  "bluish  green"  to  "yellowish  green."  The  tertiaries  are  not  so  easily  prepared. 
Russet,  for  instance,  is  a  mixture  of  violet  and  orange,  the  violet  being  a  combination  of  red 
and  blue,  and  the  orange  a  combination  of  red  and  yellow.  Thus  in  the  composition  of  russet 
the  primary  red  enters  twice  and  the  primary  blue  and  yellow  once  each.  Citrine  and  olive 


68  TOPOGRAPHICAL   DRAWING  IN   COLORS 

are,  in  a  similar  way,  found  to  consist  of  varying  proportions  of  the  three  primaries,  and  the 
relation  of  tertiaries  to  primaries  may  be  shown  as  follows :  — 

Russet  =  2  red  +  blue  +  yellow 
Citrine  —  2  yellow  +  red  +  blue 
Olive  =  2  blue  +  red  +  yellow 

The  above  is  not  intended  as  a  guide  by  which  to  mix  the  tertiary  colors.  Considerable 
experimenting  is  usually  necessary  to  obtain  the  tertiaries,  since  a  combination  of  the  three  pri- 
maries produces  neutral  tint  except  when  they  are  in  exactly  the  correct  proportions  to  pro- 
duce the  tertiaries. 

76.  Special  Combinations  of  Colors.  Colors  for  special  purposes,  or  for  greater  variety  than 
those  given  in  the  last  article,  may  be  produced  as  shown  below  :  — 

Azure,  cobalt  +  white 

Buff,  yellow  ochre  +  white  +  red 

Chestnut,  red  +  black  +  yellow 

Chocolate,  raw  umber  +  red  +  black 

Claret,  red  +  umber  -f  black 

Copper,  red  +  yellow  +  black 

Cream,  burnt  sienna  \  +  yellow  J  +  white  £ 

Dove,  vermilion  +  white  +  blue  +  yellow 

Drab,  yellow  ochre  +  white  +  red  +  black 

Flesh,  yellow  ochre  J+  vermilion  £  +  white  J 

Lemon,  chrome  yellow  +  white 

Olive,  yellow  4-  blue  +  black  +  white 


TOPOGRAPHICAL  DRAWING  IN  COLORS  69 

Peach,  vermilion  +  white 
Pink,  rose  lake  +  white 
Rose,  madder  lake  +  white 
Violet,  blue  +  red  +  white 

Greens 

Bronze,  chrome  green  +  black  +  yellow 

Dark,  Prussian  blue  +  chrome  yellow 

Olive,  lemon  yellow  +  chrome  green  +  burnt  sienna 

Pea,  chrome  green  +  white. 

Grays 

Black  +  white 
Black  +  white  +  blue 
Burnt  sienna  +  blue  +  white 
Burnt  umber  +  blue 
Payne's  gray  +  crimson  lake. 

77.  Topographical  Drawing  in  Colors.  In  color  topography  the  objects  are  in  some  cases 
suggested  by  both  form  and  color,  as  in  trees  and  buildings,  and  sometimes  by  color  only,  as 
in  grass  land.  The  advantages  derived  from  using  colors  are  that  a  map  is  produced  which 
is  more  pleasing  to  the  eye,  more  easily  read,  and  in  general,  more  quickly  made  than  when 
the  symbols  are  rendered  in  lines  only.  The  chief  disadvantage  is  that  a  map  in  colors  cannot 
be  cheaply  and  readily  reproduced,  either  by  lithography  or  blue  printing. 

As  in  pen  topography  the  size  of  symbols  will  be  varied  to  suit  the  scale  of  the  drawing. 


70  TOPOGRAPHICAL   DBA  WING  IN   COLORS 

78.  Grass  Land  is  shown  by  a  flat  tint  of  green.     P.B.  +  G.  +  Y.O.  is  suitable  for  this 
purpose.     In  meadow  land  where  clover  may  be  supposed  to  grow,  spots  of   C.L.    may   be 
introduced  by  the  method  explained  in  Art.  72. 

79.  Cleared  Land,  Plate  III,  is  shown  by  a  flat  ground  color  of  green  as  for  grass  land,  with 
a  mottling  of  B.S.  as  explained  in  Art.  72. 

80.  Cultivated  Land,  Plate  III.     A  flat  ground  tint  of  B.S.  is  first  laid  on,  and  over  this 
are  ruled  lines  of  the  same  color,  but  mixed  considerably  stronger.     For  variety  P.G.  -f  a 
very  little  C.L.  may  also  be  used  for  some  fields. 

81.  Sand  and  Gravel,  Plate  III.     For  sand  a  flat  tint  of  Y.O.  is  used,  and  gravel  is  indi- 
cated by  dots  of  B.S.  put  on  with  the  tip  of  a  small  brush  or  with  a  coarse  pen. 

82.  Mud  is  shown  by  groups  of  short  horizontal  lines  as  in  plain  topographical  drawing 
(Art.  52),  except  that  a  rather  heavy  tint  of  S.  is  used  in  the  ruling  pen  instead  of  India  ink. 
A  wash  of  S.  should  first  be  laid  over  the  whole  area  just  strong  enough  to  dim  the  whiteness 
of  the  paper. 

83.  Individual  Trees,  Plate  III,  should  first  be  plainly  outlined  in  pencil,  after  which  a 
bright,  and  decidedly  yellowish  green  composed  of  P.B.  and  G.  is  laid  over  the  whole  area. 
The  lower  right-hand  half  of  each  tree  is  then  colored  with  a  much  stronger  bluish  green. 
This  should  be  applied  with  a  rather  dry  brush,  and,  along  the  edge  which  lies  in  the  diameter 
of  the  tree,  the  touch  should  be  very  light  and  with  the  tip  of  the  brush,  so  there  will  be 
spots  here  and  there  not  covered  by  the  color.     That  is,  the  effect  along  this  line  should  be 
that  of   "  dragging  "  on  a  very  small  scale.     The  object  is  to  avoid  too  sudden  a  transition 


Cleared  Land 


Deciduous  Trees 


Cultivated  Land 


4     C 


Deciduous  Trees  in  Mass 


Sand  and  Gravel 


Evergreen  Trees  in  Mass 


Plate  III. 


FRESH   MARSH  73 

from  the  bright,  illuminated  side  to  the  side  which  is  in  shade.  Next  the  shadow,  composed 
of  P.G.  +  C.L.,  is  brushed  in.  If  this  tint  is  allowed  to  encroach  a  little  upon  the  shaded 
side  of  the  tree  itself,  the  effect  of  relief  will  be  heightened.  Last  of  all  the  curvilinear  lines 
are  drawn,  suggesting  the  rounded  outlines.  The  color  should  be  very  bright  and  strong,  and 
may  be  applied  with  a  pen  as  are  the  black  lines  shown  in  Fig.  33. 

Evergreen  Trees  may  be  shown  as  in  Figs.  33  and  34,  using  bluish  green  instead  of  ink. 

The  ground  color  for  grass  land,  cleared  land,  etc.,  is  to  be  put  on  before  the  trees  are 
drawn. 

84.  Trees  in  Mass,  Plate  III.     For  deciduous  trees  patches  of  green  are  applied  which  are 
irregular  in  shape  and  size.     This  color  should  be  of  medium  strength, -com posed  of  P.B.  + 
G.,  with  a  little  S.  added  to  deaden  the  brightness.    The  curvilinear  lines  are  of  the  same  color, 
but  considerably  stronger,  applied  with  the  tip  of  a  small  brush  or  with  a  coarse  pen. 

Evergreen  Trees  are  shown  by  the  same  method  except  that  the  final  lines  instead  of  being 
curvilinear,  are  straight,  suggesting  the  needlelike  foliage  of  pine,  spruce,  etc.  When  the 
scale  of  the  map  is  small,  it  may  be  more  effective  to  use  the  convention  for  individual  trees 
sprinkled  over  the  area  as  suggested  in  the  figure. 

85.  Fresh  Marsh,  Plate  IV.     See  also  Figs.  27  and  35.     The  irregular  patches  of  land  are 
rather  strongly  outlined  in  pencil,  and  colored  for  grass  land  or  cleared  land  as  the  case  may 
require.     The  water  surface  is  then  colored  P.B.     The  islands  are  next  given  a  stronger  out- 
line and  an  appearance  of  relief  by  adding  lines  of  a  brighter  green  at  their  upper  edges  and 
shadow  lines  at  their  lower  edges.     These  latter  lines  may  be  of  S.  or  of  I.  -f-  B.S.     Small 
trees  or  bushes  may  be  indicated  to  heighten  the  effect. 


74  TOPOGRAPHICAL  DRAWING  IK  COLORS 

Care  should  be  taken  that  the  long  stretches  in  the  outlines  are  nearly  parallel  to  the 
lower  edge  of  the  drawing. 

86.  Salt  Marsh,  Plate  IV.     The  whole  area  is  first  treated  with  the  appropriate  ground 
color,  after  which  P.B.  is  dragged  (Art.  73)  to  represent  irregular  patches  of  water.     Lines 
of  stronger  P.B.  are  then  ruled  along  the  upper  edges  of  these  patches,  and  always  parallel  to 
the  lower  edge  of  the  drawing.     The  direction  of  movement  of  the  brush  in  dragging  must 
also  be  in  this  direction. 

87.  Water,  Plate  IV.     The  method  of  representing  water  depends  upon  the  taste  of  the 
draftsman  and  upon  the  time  which  may  be  spent  upon  the  map.     A  very  delicate  effect  may 
be  obtained  by  the  method  of  water  lines  explained  in  Art.  57,  P.B.  being  used  instead  of  ink. 
The  objection  to  this  method  is  the  great  amount  of  time  required. 

A  quick,  easy,  and  often  a  satisfactory  method  is  that  shown  at  the  right  of  the  Plate, 
where  a  flat  tint  of  P.B.  is  laid  over  the  water  surfaces.  The  shore  line  is  defined,  and  relief 
secured  by  drawing  a  narrow  band  of  S.  and  blending  it  (Art.  71)  toward  the  land. 

A  more  pleasing  effect,  and  one  not  requiring  an  excessive  amount  of  time,  is  shown  in  the 
lower  left-hand  corner  of  the  Plate,  where  a  graded  tint  of  P.B.  is  laid  from  the  shore  lines. 
The  method  of  grading  explained  in  Art.  70  is  not  practicable  for  this  work. 

The  whole  width  of  the  body  of  water  is  first  covered  with  a  flat  tint  of  very  weak  P.B.  A 
wide  band  of  a  stronger  tint  is  then  laid  next  the  shore  line  and  blended  (Art.  71)  on  the  edge 
remote  from  the  shore  line.  When  the  whole  body  has  received  this  blended  band,  another  is 
laid  in  the  same  way,  but  narrower  and  in  a  still  stronger  tint.  This  process  is  repeated  as 
many  times  as  necessary  to  secure  the  desired  effect.  Finally  a  narrow  line  of  a  decidedly 


-3LJ 

* 


Fresh  Marsh 


Salt  Marsh 


Water   (i) 


Water  (2) 


Embankment  and  Cut 


Ledge 


Plate  IV. 


77 

strong  tint  is  drawn  at  the  shore  line  with  a  fine  brush  or  a  ruling  pen.     The  shore  line  may 
be  finished,  however,  with  the  blended  line  of  S.  as  explained  for  the  flat-tint  method. 

For  rather  rough  work,  such  as  field  sheets  or  preliminary  plots,  water  is  often  shown  by 
successively  narrower  and  stronger  bands  of  color  as  described  above,  but  without  blended 
edges. 

88.  Streets  and  Roads  are  colored  with  a  flat  tint  of  Y.O.,  the  edge  being  defined  by 
inked  lines  as  in  plain  drawing,  Art.  58. 

89.  Railways  are  shown  as  in  plain  drawing,  Art.  59. 

90.  Embankments  and  Cuts,  Plate  IV.     The  sloping  surfaces  are  expressed  by  a  graded 
tint  of  P.G.  +  C.L.  laid  by  the  blending  process  as  explained  in  Art.  87.      As  in  pen  drawing 
the  dark  portion  of  the  shaded  surface  is  that  nearer  the  eye  ;  that  is,  the  dark  edge  is  at  the 
top  of  the  embankment  and  at  the  outer  edge  of  the  cut.     The  top  of  the  embankment  and  the 
bottom  of  the  cut  will  be  colored  to  express  the  actual  conditions  of  these  surfaces. 

91.  Ledge,  or  Rocky  Surface.     A  fairly  strong  tint  of  S.  +  a  little  B.S.  is  dragged  over 
the  surface  to  be  covered,  the  brush  being  moved  along  the  outcrops  in  rocky  surfaces,  or  along 
the  supposed  lines  of  continuous  rock  in  ledges.     The  dragging  should  be  so  lightly  done  that 
two  or  three  applications  of  the  color  will  be  required.     Finally  the  seams  and  fissures  are 
drawn  with  the  tip  of  the  brush,  in  a  somewhat  stronger  tint. 

92.  Fences,  Walls,  and  Hedges.     Fences  and  walls  are  drawn  in  ink  as  in  plain  drawing, 
Fig.  40,  but  the  outlines  of  the  walls  are  filled  in  with  P.G.     A  hedge  is  shown  as  a  close  row 
of  small  trees  (Art.  83),  a  line  of  shadow  being  added. 


78  TOPOGRAPHICAL   DRAWING  IN   COLORS 

93.  Buildings.     The  outlines  are   drawn   in  India   ink,  shade   lines  being  used.      For 
wooden  buildings  the  area  within  the  outline  is  colored  S.,  brick  C.L.,  and  stone  is  indicated 
by  P.O. 

94.  Use  of  Colored  Pencils.     While  colored  pencils  (Art.  23)  do  not  give  the  variety  or 
delicacy  of  coloring  that  can  be  secured  with  water  colors,  they  are  of  great  convenience,  and 
in  some  cases  their  use  is  to  be  preferred  to  that  of  water  colors.     For  instance,  it  may  be 
desired  to  color  an  area  when  it  is  known  that  at  some  future  time  the  color  will  need  to  be 
changed  ;  pencil  may  then  be  used  to  advantage,  since  it  can  be  removed  with  comparative 
ease  with  a  rubber  eraser. 

A  city  map  may  have  the  streets  colored  to  show  the  various  kinds  of  pavements  in  use,  as 
red  to  indicate  brick,  and  brown  to  indicate  asphalt.  But  some  brick  pavements  may  be  re- 
placed by  asphalt,  in  which  case  it  is  desirable  to  be  able  to  change  the  coloring  easily.  Or  a 
city  may  have  both  the  "combined"  and  the  "separate"  systems  of  sewerage,  the  area 
covered  by  the  former  being  colored  green,  and  that  covered  by  the  latter,  buff.  But  if  the 
separate  system  is  replacing  the  combined,  it  is  easy  to  keep  the  record  map  up  to  date  if 
colored  pencils  are  used,  thus  making  erasures  easy. 

When  only  a  very  little  coloring  is  necessary  as  a  given  piece  of  work  progresses,  pencils 
are  much  more  convenient,  as  they  are  always  ready  for  use,  and  require  almost  no  room  as 
compared  with  the  articles  necessary  for  water  coloring.  It  is  impossible  to  enumerate,  even 
approximately,  the  cases  where  colored  pencils  may  appropriately  be  used  instead  of  water 
colors.  Each  means  of  coloring  has  its  own  sphere,  and  it  should  not  be  supposed  that  either 
can  wholly  replace  the  other. 


COLOEED  PENCILS  79 

95.  Use  of  the  Stump.     When   large  areas   are    colored  with  pencils,  it  is  desirable  to 
smooth  the  color  with  a  stump,  and  this  is  necessary  with  small  areas  also  if  the  best  result  is 
to  be  obtained. 

The  best  stump  consists  of  a  tight  roll  of  chamois  skin,  the  ends  of  which  are  cut  pointed. 
An  inferior  stump  may  be  extemporized  by  rolling  up  a  strip  of  newspaper  or  blotting  paper, 
and  holding  it  together  by  a  rubber  band.  The  end  is  then  pared  to  a  point  with  a  sharp 
knife. 

The  pencil  is  first  rubbed  lightly  over  the  surface  to  be  colored,  covering  it  uniformly,  but 
leaving  it  slightly  lighter  in  tone  than  is  finally  desired.  The  surface  is  then  rubbed  with  the 
end  of  the  stump,  which  distributes  the  color  evenly,  and  also  rubs  it  into  the  minute  depres- 
sions of  the  paper,  which  are  not  reached  by  the  pencil,  thus  deepening  the  tone. 

96.  Colored  Pencils  with  Tracing  Paper  and  Tracing  Cloth.     Sketch  maps,  architectural 
details,  and  a  great  variety  of  other  subjects  are  often  drawn  upon  tracing  paper  or  cloth,  after 
which  the  more  prominent  features  are  brought  out  with  colored  pencils.     In  such  cases,  how- 
ever, the  color  is  best  applied  on  the  back  of  the  drawing,  for  the  following  reasons  :  the  trans- 
lucency  of  the  paper  softens  the  cruder  colors;  though  the  color  is  laid  on  quite  roughly,  it  still 
looks  smooth  when  viewed  from  the  face  of  the  drawing;  the  inked  outlines  are  not  interfered 
with,  and  if  any  of  them  need  to  be  changed,  the  erasures  do  not  disturb  the  color. 

If  tracing  cloth  is  to  be  colored  with  pencils  the  drawing  should  be  made  on  the  bright 
side,  leaving  the  dull,  rough  back  to  receive  the  color. 

An  advantage  in  favor  of  pencils  for  coloring  upon  thin  paper  or  cloth  is  that  they  do  not 
cause  buckling  or  wrinkling  as  water  colors  do. 


80  TOPOGRAPHICAL  DRAWING  IN  COLORS 

97.  Colors  in  relation  to  Blueprinting.     If  blueprints  are  to  be  made  from  drawings  on 
cloth  or  thin  paper,  it  is  well  to  avoid  the  use  of  blue  color,  or  of  secondary  colors  in  which  blue 
predominates,  as  these  colors  are  transparent  to  the  chemical  rays  by  which  the  printing  is 
done.     Of  course  it  is  desirable  to  use  blue  for  water,  but  it  should  be  laid  on  very  heavily, 
and  it  will  always  be  more  prominent  on  the  drawing  than  its  effect  will  be  on  the  print. 

On  the  other  hand,  yellow,  orange,  and  red  print  well,  and  yellowish  green  and  reddish 
violet  print  fairly  well. 

98.  Colored  Whiteprints.     A  common,  and  very  satisfactory  method  of  securing  several 
copies  of  a  colored  drawing  is  to  make  the  outlines  upon  tracing  cloth,  from  which  prints  are 
taken  showing  either  black  lines  on  a  white  ground  or  blue  on  white  (Art.  138).     These  are 
then  colored  as  desired,  either  with  water  colors  or  with  pencils. 

If  the  drawings  are  to  be  used  frequently,  they  should  be  mounted  on  cloth  (Art.  30) 
after  being  colored,  and  this  should  always  be  done  if  water  colors  have  been  used,  as  the 
surface  will  otherwise  remain  more  or  less  wrinkled.  If  the  mounting  is  carefully  done,  the 
coloring  need  not  be  injured  by  the  process. 

Prints  showing  black  lines  on  a  white  ground  often  prove  disappointing  when  mounted, 
as  the  paste  used  in  the  work  may  gradually  turn  the  paper  a  dirty  pinkish  color  which  is  likely 
to  have  an  undesirable  effect  upon  colors  previously  applied. 

EXERCISES  IN  WATER  COLORING 

99.  General  Directions.     The  following  exercises  are  to  be  performed  on  Whatman's  cold- 
pressed  paper  (Art.  17)  stretched  upon  the  drawing  board  (Art.  29).     The  sheets  will  be 
11  x  15  inches,  with  border  line  10  x  14  inches. 


EXERCISES   IN   WATER   COLORING  81 

It  is  desirable  to  stretch  a  sheet  large  enough  to  make  two  or  more  of  the  finished  sheets. 
Atlas  paper,  26  x  34  inches,  will  make  four  of  the  small  sheets  with  only  as  much  waste  at 
the  margins  as  is  desirable  for  stretching  and  for  trying  the  colors. 

100.  Exercise  in  Flat  Tints.     Divide  a  sheet  into  six  rectangles  such  that  there  shall  be 
one  half  inch  between  adjacent  rectangles,  and  between  each  rectangle  and  the  border  line. 

Color  the  three  upper  rectangles  with  primary  colors  in  this  order  :  1,  G.  ;  2,  C.L. ; 
3,  P.B.  The  student  must  remember  that  the  tints  are  to  be  kept  light,  also  that  it  is  easier 
to  lay  a  flat  tint  if  it  is  light  than  if  it  is  heavy.  Of  the  three  colors  named  above  the  P.B.  is 
most  liable  to  give  trouble,  and  the  student  is  advised  to  apply  two  very  light  washes  rather 
than  a  single  one  of  the  required  strength. 

Color  the  three  lower  rectangles  with  secondary  colors  in  this  order  :  4,  Violet  (C.L.  + 
P.B.)  ;  5,  Green  (G.  +  P.B.)  ;  6,  Orange  (G.  +  C.L.). 

Note  that  each  secondary  color  is  composed  of  those  primaries  which  are  not  above  it, 
and  that  it  "  harmonizes  "  with  that  primary  which  is  above  it. 

101.  Exercise  in  Graded  Tints  and  in  Mottling.     Divide  a  sheet  as  for  the  last  exercise. 

In  the  three  upper  rectangles  lay  graded  tints  (Art.  70)  of  the  following  colors  in  order  : 
1,  P.G.  ;  2,  Y.O.  ;  3,  S. 

The  lower  rectangles  are  to  be  colored  as  follows,  in  order  :  4,  Green  mottled  (Art.  72) 
with  C.L.  ;  5,  B.S.  mottled  with  P.G.  with  a  very  little  C.L.  added  ;  6,  Orange  mottled 
with  Violet. 

102.  Exercise  in  Conventional  Tints  and  Symbols.     Divide  a  sheet  as  shown  for  Plate  I, 
Art.  64.     Taking  the  nine  rectangles  in  order  from  left  to  right,  show  in  them  the  follow- 


82  TOPOGRAPHICAL  DRAWING  IN   COLORS 

ing,  the  numbers  in  parentheses  referring  to  the  articles  which  should  be  read  carefully  (in  ad- 
dition to  a  study  of  Plates  III  and  IV),  before  the  coloring  work  is  begun  :  - 

1.  Grass  land  (78). 

2.  Cleared  land  (79,  72). 

3.  Cultivated  land  (80). 

4.  Sand,  gravel,  and  mud  (81,  82,  52).     Show  an  area  of  gravel  in  the  upper  left-hand 

corner,  and   one  of  mud  in   the   lower  right-hand  corner.     The  color  for  sand 
should  be  blended  with  the  ground  color  for  the  mud. 

5.  Individual  deciduous  trees  (83).     Arrange  in  rows  ^  inch  apart,  and  space  ^-  inch  in 

the  rows.     The  first  row  is  to  be  |-  inch  from  the  top  of  the  rectangle,  and  the 
first  tree  in  each  row  £  inch  from  the  left-hand  edge. 

6.  Deciduous  trees  in  mass  (84). 

7.  Evergreen  trees  in  mass  (84). 

8.  Fresh  marsh  (85). 

9.  Salt  marsh  (86). 

103.     Exercise  in  Conventional  Tints  and  Symbols  (continued).     The  sheet  is  to  be  divided 
as  for  the  last  exercise. 

1.  Water,  blue  water  lines  (87,  57). 

2.  Water,  flat-tint  method  (87). 

3.  Water,  graded-tint  method  (87). 

4.  Embankment  (90). 

5.  Cut  (90). 


APPLICATION   OF  CONVENTIONAL   TINTS  AND   SYMBOLS  83 

6.  Rocky  surface  (91). 

7.  Fence,  walls,  and  hedge  (92),  drawn  horizontally  across  the  rectangle. 

8.  Streets  and  roads  (88,  58),  and  railways  (89,  59). 

9.  Buildings  (93,  63)  of  wood,  brick,  and  stone.     Draw  two  of  each,  of  different  shapes, 

and  arrange  the  whole  in  two  horizontal  lines. 

104.  Application  of  Conventional  Tints  and  Symbols.  As  an  exercise  in  bringing  the 
tints  and  symbols  together  in  a  map  the  student  may  use  the  outlines  of  Plate  II,  or  may  invent 
a  similar  map  for  himself.  An  actual  survey  may  also  furnish  excellent  outlines,  and  be  of 
special  interest  beside  ;  but  it  is  seldom  that  an  actual  survey  of  so  small  an  area  as  is  desir- 
able for  this  exercise  will  give  opportunity  for  the  use  of  all  the  conventional  tints  and  symbols. 


CHAPTER   VI 

SURFACE  FORMS  AND   EARTHWORK 

SECTION  I.     SURFACE  FORMS 

105.  Representation  of  Surface  Forms.  In  many  engineering  operations  it  is  necessary 
to  gain  exact  knowledge  of  the  conformation  of  the  surface  of  the  ground.  First  of  all,  a  sur- 
vey is  necessary  to  establish  the  relative  heights  of  as  many  points  on  the  ground  as  the  problem 
in  hand  may  require.  As  a  common  starting  point  from  which  to  measure  such  heights,  a 
level  plane  is  chosen,  in  general  lower  than  the  lowest  point  on  the  ground  whose  height  is  to 
be  determined.  Such  a  plane  is  called  a  datum,  and  is  usually  taken  at  average  mean  tide  in 
localities  where  the  sea  is  accessible  ;  in  other  localities  an  arbitrary  datum  is  assumed.  It  is 
customary  to  speak  of  the  relative  height  of  a  point  as  its  elevation.  Thus  if  a  point  is  marked 
"  El.  173.6,"  the  meaning  is  that  it  is  173.6  feet  above  the  datum  which  is  used  for  that  survey. 
If  there  be  any  doubt  or  misunderstanding  as  to  what  the  datum  is,  the  drawing  should  con- 
tain a  note  of  explanation. 

In  sub-surface  work,  such  as  waterworks,  sewer  or  dock  construction,  many  points  lie 
below  the  datura,  and  their  relative  heights  are  given  with  the  minus  sign  prefixed ;  thus 
"El.  —  15.13"  means  that  the  point  is  15.13  feet  below  the  datum.  There  is  always  danger 
that  a  minus  elevation  will  be  mistaken  for  a  plus  elevation,  and  for  this  reason  it  is  not  un- 

84 


REPRESENTATION   BY   PROFILE  85 

common,  where  much  sub-surface  work  is  to  be  done,  to  assume  the  datum  100  feet  below 
that  which  is  ordinarily  used,  so  that  no  confusion  may  result,  since  all  elevations  will  be 
positive. 

When  many  elevations  are  recorded  on  a  plan,  and  no  doubt  is  possible  as  to  the  mean- 
ing, the  figures  alone  are  written,  without  even  the  abbreviation  for  "elevation." 

The  exact  point  whose  elevation  is  recorded  is  marked  by  the  decimal  point  in  the  num- 
ber expressing  the  elevation,  unless  the  point  is  plainly  shown  otherwise. 

106.  Representation  by  Recorded  Elevations.     The  readiest  means  for  representing  sur- 
face form  is  by  securing  elevations  of  many  points  scattered  over  the  area,  and  recording 
them,  as  described  above,  upon  a  plan  of  that  area.     It  is  then  readily  seen  whether  a  given 
point  in  a  region  is  higher  or  lower  than  one  in  another  region.     But  the  surface  must  be 
studied  point  by  point,  as  the  method  does  not  present  to  the  eye  an  idea  of  the  surface  as  a 
whole  ;  hence  it  is  not  generally  used  except  for  very  limited  areas,  such  as  house  lots. 

107.  Representation  by  Profile.     When  it  is  of  interest  to  know  the  form  of  surface 
merely  along  a  definite  line,  such  as  the  center  of  a  street  or  of  a  water  pipe,  the  representa- 
tion is  usually  made  by  means  of  a  profile,  which  may  be  defined  as  the  intersection  of  a  ver- 
tical plane  with  the  earth's  surface  or  with  other  objects  which  are  to  be  shown. 

Fig.  46  shows,  to  a  reduced  scale,  a  profile  drawn  on  "Plate  A  "  paper  (Art.  17).  Note 
that  the  drawing  would  be  of  excessive  height  if  it  were  carried  down  to  show  the  datum, 
that  is,  down  to  El.  0.0.  In  such  a  case  a  line  parallel  to  the  datum,  and  at  a  convenient  dis- 
tance above  it,  is  chosen  from  which  to  construct  the  profile.  Such  a  line  is  called  a  base  line. 


86 


SURFACE  FORMS  AND  EARTHWORK 


The  stations  are  marked  along  the  base  line.  These  are  points  at  the  extremities  of  100- 
foot  distances  measured  horizontally  along  the  line  on  which  the  profile  is  taken.  If  the  scale 
is  large,  as  40  feet  to  1  inch,  each  station  point  is  usually  numbered  ;  if  the  scale  is  small, 
only  every  fifth  or  tenth  station  need  be  marked.  Any  point  between  even  stations  is  called 

a  plus;  thus  a  point  at  530.6 
feet  beyond  Sta.  0,  the  begin- 
ning of  the  profile,  is  called 
point  5  +  30.6,  or  its  position  is 
said  to  be  at  Sta.  5  +  30.6. 

It  is  generally  desirable 
that  all  irregularities  and 
changes  in  direction  of  the  sur- 
face lines  of  the  ground  shall 
be  very  marked.  Consequently 
a  different  scale  is  used  in  lay- 
Fig.  46.  jng  Off  elevations  above  the  base 

line  from  that  used  in  laying  off  the  stations,  and  profile  paper  is  ruled  to  facilitate  the  making 
of  such  "exaggerated"  profiles.  If  the  surface  is  very  irregular  and  precipitous,  the  same 
scale  may  be  used  for  both  horizontal  and  vertical  distances,  and  such  a  representation  is  a 
"natural"  profile. 


68 
67 
66 

RK 

=P 

^2 

^ 

64 
63 
62 
61 
60 

( 

) 

M 

+87 

^ 

* 

35.> 

1- 

» 

The  scale  of  exaggeration  is  the  ratio  of  the  number  of  feet  shown  horizontally  per  unit 
distance  on  the  paper  to  the  number  of  feet  shown  vertically  to  the  same  unit.     Thus  if  the 


REPRESENTATION   BY   CONTOUR  LINES  87 

horizontal  scale  is  40  feet  to  1  inch,  and  the  vertical  scale  is  4  feet  to  1  inch,  the  scale  of 
exaggeration  is  40  -4-  4  =  10,  which  is  the  scale  shown  in  the  figure,  and  is  very  commonly  used. 
Since  the  rulings  on  profile  paper  are  in  color,  and  rather  faint,  the  profile  line  itself 
stands  out  more  clearly  than  is  shown  by  Fig.  46,  and  the  surface  line  is  often  accentuated  by 
drawing  a  band  of  color  immediately  beneath  it. 

108.  Cross-Sections.     When  a  vertical  section  such  as  is  described  above  is  taken  at  right 
angles  to  the  line  of  a  profile,  or  across  any  well-defined  longitudinal  feature,  such  as  a  stream, 
cut,  or  embankment,  the  representation   is  called  a  cross-section.     The  lines  shown  in  such 
a  representation  usually  make  well-marked  angles  with  one  another  and  no  exaggeration  is 
necessary.     Therefore  cross-section  paper  (Art.  17)  has  the  vertical  and  horizontal  rulings 
to  the  same  scale. 

109.  Representation  by  Contour  Lines.     It  is  evident  that  none  of  the  foregoing  methods 
of  showing  surface  form  are  suitable  for  giving  even  a  general  idea  of  the  configuration  of  a 
considerable  area.     An  adequate  method  must  show  at  a  glance  the  relative  steepness  of  the 
surface  along  any  line,  and  must   also  furnish  means  of  obtaining  readily  and  closely  the 
distance    horizontally  and  vertically  from  any  one   point  to  another,  and  the   angle   which 
any  line  in  the  surface  makes  with  a  horizontal  plane  —  that  is,  the  declivity  of  the  surface 
along  that  line. 

Such  a  method  is  found  in  the  use  of  contour  lines,  which  are  drawn  directly  upon  the 
plan  of  the  area,  forming  a  contour  map,  which  is  the  basis  for  many  designs  and  operations 
in  engineering. 


88 


SURFACE  FORMS  AND  EARTHWORK 


»o  -ft 


A;B 


Datum 


C!D 


Fig.  47  shows  a  pyramid  whose  base  is  square  and  10  feet 
above  datum,  and  which  is  intersected  by  a  series  of  horizontal 
planes  parallel  with  the  datum  plane,  and  spaced  5  feet  apart  verti- 
cally. These  planes  intersect  the  surface  of  the  pyramid  in  squares 
which  are  shown  projected  into  the  plan.  If,  now,  there  be  written 
upon  each  of  these  intersections  in  plan  the  number  (called  the 
reference  number,  or  simply  reference)  which  shows  its  height  above 
the  datum,  the  information  concerning  the  size  and  form  of  the 
figure  is  complete  on  the  plan  alone ;  for  the  shape  and  size  of  the 
base  and  the  position  of  the  apex  show  the  general  form  of  the  figure 
and  its  dimensions  in  plan,  while  the  intersections  of  the  cutting 
planes,  with  their  references,  indicate  clearly  the  height  of  the 
figure  and  the  nature  of  the  sloping  surfaces. 

This  last  statement  may  need  further  explanation.  By  study- 
ing the  elevation  and  plan  together  the  several  facts  will  become 
evident.  But  for  convenience  let  it  first  be  stated  that  what  have 
been  called  "  intersections  of  the  cutting  planes  with  the  surface  " 
are  contours,  and  a  definition  of  a  contour  may  be  established  as  the, 
intersection  of  a  level  plane  with  the  surface  of  the  earth  or  other  object 


Fig.  47. 

through  which  it  may  be  supposed  to  pass. 

For  further  convenience  let  it  be  stated  that  contours  are  given  the  names  of  their 
reference  numbers;  thus  "contour  25  "means  the  contour  whose  reference  number  indicates 
that  it  is  25  feet  above  datum. 


INTERPOLATION   OF  CONTOURS  89 

The  figure  shows  that  the  face  COD  makes  a  greater  angle  with  the  horizontal  base  than 
does  the  face  AOB  ;  that  is,  it  is  steeper.  This  is  shown  in  the  plan  by  the  fact  that  the 
contours  are  closer  together  between  O  and  CD  than  between  O  and  AB.  Hence  the  closer 
together  the  contours  in  the  same  plan,  the  steeper  the  surface. 

But  it  is  often  desirable  to  know  definitely  how  steep  a  surface  is.  The  line  cb  is  a  por- 
tion of  the  projecting  line  of  contour  20,  and  is  therefore  vertical,  and  dbc  is  a  right  triangle  in 
which  cb  is  the  vertical  distance  between  contours  15  and  20,  and  ab  is  the  horizontal  distance 

cb 
between  the  same  contours  as  shown  in  plan.     But  — r  =   tan  of  cab,  which  is  the  "  angle  of 

greatest  declivity  "  of  the  surface  between  contours.     Hence  the  tangent  of  the  angle  express- 

vertical  distance  between  contours 

ing  the  steepness  of  the  surface  is  the  ratio,  , : t  ,   ,.  J : — - - •     Jn  general 

horizontal  distance  between  contours 

the  horizontal  distance  must  be  scaled  from  the  plan,  while  the  vertical  distance  is  the  differ- 
ence between  the  references  of  the  adjacent  contours. 

By  a  comparison  of  triangles  abc  and  cde  it  can  be  shown  that  ab  =  cd,  and  that  therefore 
the  corresponding  contours  are  equidistant.  In  the  same  way  it  can  be  demonstrated  that 
equidistance  exists  among  all  the  contours  on  this  surface,  as  shown  in  plan.  Therefore  if  a 
series  of  contours  are  straight  and  equidistant,  the  surface  in  which  they  lie  is  a  plane  surface. 

The  student  will  readily  discover  the  forms  of  contours  which  express  other  regular  surfaces, 
and  so  be  prepared  to  interpret  the  contours  which  express  the  irregular  surfaces  of  the  ground. 

110.  Interpolation  of  Contours.  The  information  as  to  the  topography  of  the  ground  is 
furnished  by  the  surveyor  in  different  forms,  according  to  various  circumstances.  By  some 


90 


SURFACE  FORMS  AND  EARTHWORK 


field  methods  the  contours  are  drawn  directly  on  the  "  field  sheets  "  used  by  the  surveyor,  or 
notes  are  furnished  by  which  the  contours  are  plotted  by  the  draftsman  without  intermediate 
processes  such  as  those  described  below  ;  but  in  general,  economy  dictates  that  a  rapid  method 
of  survey  be  adopted,  and  this  means  that  the  notes  furnished  will  not  enable  the  draftsman  to 
draw  the  contours  directly,  but  will  inform  him  as  to  the  location  of  points  of  known  eleva- 
tion, either  regularly  spaced,  as  in  Fig.  48,  or  scattered 
more  or  less  at  random.  The  interpolation  of  contours  is 
the  process  of  drawing  the  contours  among  these  points 
from  their  established  elevations, 


5?.8 


52.4 


Fig.  48. 


111.     Interpolation  from  Corners  of  Rectangles.     In 

some  cases  the  ground  is  divided  into  rectangles  or 
squares,  and  elevations  are  taken  at  the  corners,  as 
shown  in  Fig.  48.  When  the  observed  elevations  are 
thus  regularly  spaced,  the  contours  may  be  interpolated 
rapidly  by  means  of  the  diagram  shown  in  Fig.  49, 
which  relates  particularly  to  line  EH  of  Fig.  48.  EE,  FF,  etc.  are  vertical  lines  whose  dis- 
tances apart  are  equal  to  EF,  FG,  etc.  of  Fig.  48.  Across  these  vertical  lines  are  drawn  hori- 
zontal lines  spaced  to  some  scale  to  represent  the  desired  vertical  distances  between  the  contours, 
in  this  case  2  feet,  as  shown  by  the  numbers  48,  50  ...  62. 

On  EE  is  laid  off  the  elevation  of  point  E,  Fig.  48,  viz.  53.0,  On  FF  is  laid  off  the 
elevation  of  point  F,  and  so  on  for  points  G  and  H.  Through  the  points  thus  established  a 
smooth  free-hand  curve  is  drawn  as  shown. 


91 


The  horizontal  lines  48,  50,  etc.,  are  spaced  by  a  larger  scale  than  is  used  to  lay  off  the 
distances  EF,  FG,  etc.,  hence  the  curved  line  above  mentioned  is  an  exaggerated  profile  along 
the  line  EH,  and  cuts  the  various  level  lines  in  points  1,  2,  3,  etc.,  which  are  contour  points 
whose  distances  from  EE  are  the  respective  distances  from  E  along  EH,  Fig.  48,  at  which 
the  contours  54,  56,  58,  and  60  cross  EH. 

Similar  profiles  are  made  for  lines  AD  and  IL,  and  the  contour  points  having  the  same 
references  are  suitably  joined  and  numbered,  thus  obtaining  the  finished  contour  map. 

To  copy  the  points  1,  2,  3,  etc.,  of  Fig.  49  in  their  proper  positions  in  Fig.  48  the  follow- 
ing method  is  advisable  :  Place  the  edge  of  a  piece  of  paper  along  the  line  54  and  on  it  mark 
the  position  of  EE,  and  points  1  and  8 ;  shift  the  paper 
vertically  to  line  56  and  mark  the  position  of  points  2 
and  7.  By  further  shifting  the  paper  secure  the  posi- 
tions of  points  3  and  6,  4  and  5.  Now  lay  this  tick 
strip  with  its  edge  along  EH,  Fig.  48,  with  the  point 
which  marks  the  position  of  line  EE  placed  at  E. 
With  a  pencil  mark  the  positions  of  1,  2  ...  8  on  EH. 
But  instead  of  marking  them  1,  2,  3,  etc.,  use  the  ref- 
erence numbers  of  the  contours  to  which  they  belong.  „„ 

There  will  be  an  occasional  contour  which  will  not 

be  fully  located  by  the  above  operation,  as  contour  52,  ^' 

Fig.  48,  in  which  case  one  or  both  of  two  things  may  be  done.  A  profile  may  be  constructed 
from  the  elevations  at  A,  E,  and  I,  which  will  give  a  point  of  the  52  contour  on  line  AE;  or 
the  profile,  Fig.  49,  may  be  continued,  as  shown  in  dotted  line,  beyond  EE  to  an  intersection 


92  SURFACE  FORMS   AND  EARTHWORK 

with  the  52  level  at  w,  and  the  distance  from  n  to  line  EE  is  then  laid  off  from  E  on  FE 
extended,  Fig.  48,  thus  giving  point  n,  toward  which  contour  52  is  drawn. 

In  practice  the  diagram,  Fig.  49,  should  be  drawn  on  profile  paper.  The  vertical  lines 
should  be  inked,  so  that  when  one  profile  has  been  drawn  in  pencil  and  its  results  trans- 
ferred to  the  contour  map,  it  may  be  erased,  leaving  intact  the  necessary  lines  of  the  diagram 
for  another  profile.  Indeed,  several  profiles  may  usually  be  drawn  overlapping  each  other, 
before  undue  confusion  arises, 

It  must  be  remembered  that,  in  general,  the  corners  of  squares  are  not  points  at  which 
there  are  sudden  changes  in  the  surface;  instead,  they  are  points  on  a  smoothly  curved  surface, 
and  the  profile  must  be  so  smoothly  drawn  that  if  the  points  should  be  erased  afterward,  the 
line  would  not  indicate  the  places  where  they  had  been.  The  profile  may  pass  above  the 
highest  and  below  the  lowest  of  the  points.  A  rather  soft  pencil  should  be  used,  and  the  line 
sketched  alternately  in  both  directions  till  a  smooth,  continuous  result  is  reached. 

112.  Interpolation  on  the  Assumption  of  Straight  Grades.  It  is  often  assumed  that  the  sur- 
face line  is  straight  between  adjacent  corners  of  rectangles,  in  which  case  the  curved  profile 
of  Fig.  49  would  be  replaced  by  three  straight  lines,  one  of  which,  PR,  is  shown.  This 
would  give  very  different  positions  for  the  contour  points  from  those  obtained  from  the  curved 
line  which  represents  the  more  probable  form  of  the  ground. 

When  the  ground  is  not  rugged,  and  especially  when  the  points  whose  elevation  have  been 
determined  are  scattered  without  order  over  the  plan,  the  assumption  of  straight  grades  from 
point  to  point  is  usually  made  in  interpolating  the  contours.  Many  methods  for  making  the 
interpolations  have  been  devised,  but  the  principle  involved  is  that  of  similar  right  triangles. 


SUMMAEY  OF  PRINCIPLES  KEGAKDING  CONTOUKS  93 

For  instance,  suppose  two  points,  A  and  B,  to  be  at  elevations  18.3  and  29.6  respectively, 
and  that  they  are  300  feet  apart  horizontally  ;  also  that  even-numbered  contours  2  feet  apart 
are  to  be  interpolated.  The  vertical  distance  between  A  and  B  is  11.3  feet,  and  the  vertical 
distance  from  A  to  the  first  contour  point,  viz.  20,  is  1.7  feet.  If  x  be  the  required  distance 
in  plan  from  A  to  contour  point  20,  we  shall  have  the  following  equation:  x  =  1.7  x|^.^.  In 
the  same  way  the  distance  from  A  to  the  last  contour  point,  viz.  28,  is  #'  =  9.7  x^j.^.  The  in- 
termediate contour  points  would  now  be  inserted  by  any  convenient  method  so  as  to  make 
four  equal  spaces  from  20  to  28. 

113.  Summary  of  Principles  regarding  Contours.  The  first  seven  of  the  following  prin- 
ciples depend  upon  geometrical  conditions,  the  remainder  upon  engineering  practice. 

1.  All  points  in  the  same  contour  line  are  at  the  same  elevation. 

2.  Equally  distant  contours   show  uniformly  sloping  ground,  and  when  they  are  also 
straight  they  show  that  the  ground  is  a  plane  surface. 

3.  Contours  do  not  cross  each  other.     When  they  run  together,  they  indicate  a  vertical 
surface. 

An  exception  to  the  first  statement  might  be  shown  in  the  case  of  a  combination  of  hillside 
and  overhanging  ledge,  but  in  practice  the  contours  are  run  together  at  the  ledge  as  if  its  face 
were  vertical. 

4.  Every  contour  closes  upon  itself  or  disappears  at  the  borders  of  the  drawing,  except 
that  if  it  reaches  a  stream,  practice   dictates  that  it  shall  not  be  shown  between  the 
shore  lines. 

5.  Contours  are  normal  to  lines  of  greatest  declivity  and  to  ridge  and  valley  lines. 


94  SURFACE  FORMS  AND  EARTHWORK 

6.  No  single  contour  line  lies  between  two  higher  or  two  lower  ones,  but  two  contours 
with  the  same  reference  may  do  so,  indicating  either  a  valley  or  a  ridge. 

A  possible,  though  improbable,  exception  to  the  first  statement  is  an  instance  in  which  a 
ridge  or  valley  line  is  perfectly  level  and  at  exactly  a  contour  elevation. 

7.  A  contour  map  can  be  constructed  from  a  sufficient  number  of  profiles,  and  a  profile  on 
any  line  of  such  a  map  can  be  constructed  from  the  contours  and  scaled  distances. 

8.  The  same  equidistance  should  be  used  between  contours  in  every  part  of  the  same 
map.     If  for  a  special  reason  it  seems  desirable  to  insert  auxiliary  contours,  they  should 
be  shown  dotted  or  in  a  color  different  from  that  used  for  the  main  system. 

9.  A  break  should  be  made  in  each  contour  (or  more  than  one  if  the  contour  is  long)  for 
the  insertion  of  the  reference.     If,  however,  the  surface  is  very  flat,  so  that  contours  are 
far  apart,  it  is  better  to  put  the  references  on  the  high  side  of  the  contours. 

10.  For  greater  ease  in  reading  a  map  a  portion  of  the  contours  should  be  shown  by 
heavy  lines.     For  instance,  if  contours  2  feet  apart  are  shown,  all  those  whose  references 
are  divisible  by  10  are  drawn  heavy. 

11.  The  technical  color  for  contour  lines  is  burnt  sienna,  though  black  is  often  used  if  the 
map  is  to  be  blueprinted,  photographed,  or  lithographed. 

114.  Determination  of  Slopes  and  their  Intersections.  In  grading  ground  for  pleasing 
effect,  as  in  landscape  architecture,  rolling  surfaces  are  almost  wholly  used.  But  in  many 
engineering  works  it  is  necessary  to  use  plane  surfaces,  and  these  are  often  made  as  steep  as 
the  nature  of  the  soil  will  allow  with  safety.  Such  slopes  are  called  formal  slopes,  and  the 
steepness  is  expressed  by  the  ratio  of  the  horizontal  base  to  the  height.  Thus  a  2  to  1  (or  2  :  1) 


DETERMINATION   OF   SLOPES   AND   THEIR  INTERSECTIONS 


95 


slope  is  of  such  steepness  that  if  its  line  of  greatest  declivity  be  taken  as  the  hypotenuse  of  a 
right  triangle,  the  base  will  be  twice  the  altitude.  This  ratio  is  the  cotangent  of  the  slope 
angle,  hence  a  2  :  1  slope  is  found  to  be  at  26|°  with  the  horizontal,  a  1|  :  1  slope  at  about 
33 j°,  etc.  Toshowa2:  1 
slope,  for  instance,  by 
means  of  contours  it  is 
only  necessary  to  draw 
the  latter  straight,  paral- 
lel, and  twice  as  far  apart 
to  scale  as  the  vertical 
distance  assumed  between 
them. 

Fig.  50  shows  an  em- 
bankment whose  top  is  20 
feet  wide,  and  level  trans- 
versely, while  it  rises  to 
the  right  6  feet  in  each 
100  feet  of  length  meas- 
ured horizontally.  This 
is  equivalent  to  saying 
that  its  slope  is  1  :  16^; 
but  the  longitudinal  slope, 
or  grade,  of  roads,  etc.,  is  Fig.  50. 


96  SUKFACE  FORMS  AND  EARTHWORK 

usually  given  in  per  cent;  thus  we  should  say  that  the  top  of  this  embankment  has  a  6  per 
cent  grade.  The  side  slopes  are  1|  :  1,  and  the  natural  surface  on  which  the  embankment  is 
constructed  is  as  shown  by  the  contours  which  are  drawn  full  outside  the  embankment  and 
dotted  beneath  it. 

In  constructing  such  a  figure  we  should  have  the  natural  contours  to  start  with.  Then 
having  determined  the  starting  point,  direction,  and  top  width  of  the  embankment,  the  side 
lines  A  and  B  of  the  top  may  be  drawn.  The  contours  68,  70,  etc.,  are  next  drawn  across  the 
top  at  the  proper  intervals  to  express  the  required  per  cent  of  grade.  The  intersection  of 
these  contours  with  the  side  lines  of  the  top  are  points  in  the  contours  which  express  the  side 
slopes,  and  whose  direction  must  next  be  determined.  From  C  the  shortest  distance  to  the 
next  lower  contour  is  1|  x  2  =  3  feet,  while  from  C  to  E  is  33J  feet.  Triangle  CDE  is  there- 
fore right-angled  at  D,  and  -g-^-g-g  =  sin  CED,  from  which  the  direction  of  ED,  which  is  a 
portion  of  a  required  contour,  may  be  determined. 

A  graphical  method  of  determining  the  direction  of  the  side-slope  contours  is  generally 
preferable.  From  C  as  a  center,  and  an  opening  in  the  dividers  equal  to  several  spaces  between 
contours,  as  six,  strike  an  arc  fg.  Then  from  F,  which  is  the  sixth  contour  point  back  from  C 
at  the  top  of  the  slope,  draw  FG  tangent  tofg.  Triangle  CGF  is  similar  to  CDE,  but  is  taken 
large  for  greater  accuracy. 

The  side-slope  contours  are  now  drawn  and  numbered.  Those  which  do  not  start  from 
the  top  of  the  slope  are  at  first  drawn  of  indefinite  length  in  pencil.  The  definite  length  of 
any  one  of  these  is  determined  by  the  point  or  points  in  which  it  intersects  a  natural  contour 
of  the  same  number.  Such  an  intersection  is  also  a  point  on  the  toe  of  the  slope,  and  the 
irregular  line  HK  joining  all  such  intersections  is  the  toe  of  the  slope,  which  must  not  be 


METHOD   BY  FOUR-SIDED   PEISMS  97 

confounded  with  a  contour  line,  for  it  is  the  line  of  intersection  between  the  natural  surface 
and  the  formal  side  slope  of  the  embankment. 

Contours  of  formal  slopes  may  be  ruled,  but  for  other  surfaces,  even  though  quite  regular, 
they  should  be  drawn  free-hand. 

SECTION   II.     EARTHWORK 

115.  General  Statement.     A  very  large  item  in  many  engineering  operations  results  from 
the  removal  of  earth  in  the  construction  of  foundations,  railway  cuts,  reservoirs,  sewerage  and 
waterworks,  etc.,  and  from  the  placing  of  earth  in  new  positions,  as  in  the  building  of  roads, 
earth  dams,  railway  and  reservoir  embankments,  and  in  the  grading  of  areas. 

Payment  for  earthwork  is  usually  by  the  number  of  cubic  yards  handled,  hence  the  impor- 
tance of  methods  by  which  volumes  of  earth,  often  of  irregular  form,  may  be  determined. 

The  following  are  some  of  the  methods  in  common  use.  The  method  to  be  adopted  in 
any  case  will  depend  upon  the  general  form  of  the  volume,  and  sometimes  upon  the  degree  of 
accuracy  desired. 

116.  Method  by  Four-sided  Prisms.     When  an  area  of  approximately  rectangular  form  is 
to  be  excavated  or  filled,  it  may  be  divided  into  squares  or  rectangles  of  20  to  100  feet  on  a  side, 
and  the  volume  of  cut  or  fill  within  each  square  or  rectangle  treated  as  a  four-sided  prism. 
The  elevations  at  the  corners  are  obtained  before  work  is  commenced,  and  again  after  it  is 
finished  ;  the  difference  at  any  corner  is  the  height  of  an  edge  of  a  prism,  the  area  of  whose 
right  section  is  that  of  the  square  or  rectangle  laid  out  on  the  surface. 


98 


SURFACE   FORMS  AND  EARTHWORK 


a      b 
A 
c      d 

4 

4 

3         1 

z 

4 

4 

4        2 

2 

4 

4 

4       2 

1 

2 

I 

2         1 

Fig.  51. 

at  the  intersections. 


Suppose  the  area,  Fig.  51,  to  be  divided  into  squares  as  shown, 
that  excavation  be  made  over  the  whole  area,  and  that  the  depth  of 
excavation  be  determined  at  each  corner,  as,  a,  5,  <?,  d.  Then  if  A  be 
the  area  of  the  square  in  square  feet,  the  volume  of  excavation  in  cubic 
yards  is  A  a+b+c+d 

~27X  4 

Each  square  might  be  treated  in  this  way  and  the  results  added 
for  total  volume,  but  the  work  may  be  shortened  by  the  use  of  an 
equation  which  provides  at  once  for  the  fact  that  many  of  the  corners 
are  common  to  two  or  more  squares,  as  shown  by  the  figures  written 

This  is 

A 


V  = 


4  x27 


+ 


+  32  h3  +  42  hi"), 


in  which  A  is  the  ^area  of  one  square,  2  is  the  symbol  for  "  sum  of,"  and  hv  hv  etc.,  are  corner 
heights,  the  subscripts  indicating  the  number  of  times  each  is  taken  because  of  its  being  common 
to  1,  2,  3,  or  4  squares. 

117.  Method  by  Three-sided  Prisms.  The  method  last  stated  assumes  that  the  bases  of  the 
prisms  are  plane  surfaces,  whereas  the  upper  bases,  at  least,  are  likely  to  be  otherwise. 

It  is  always  possible  to  pass  a  plane  through  three  given  points.  If  a  diagonal  be  drawn 
to  each  square  of  Fig.  51,  we  shall  have  the  volume  divided  into  triangular  prisms,  and  it  is 
safer  than  in  the  case  of  square  prisms,  to  assume  that  their  bases  are  planes.  After  the 
ground  is  staked  out  each  square  should  be  examined  to  determine  which  of  its  two  diagonals 
should  be  chosen  so  that  the  upper  bases  of  the  resulting  triangular  prisms  shall  lie  as  nearly 


THE   PKISMOIDAL   METHOD 


99 


as  possible  in  a  plane.     Fig.  52  shows  that  corner  heights  may  be  com- 
mon to  triangular  prisms  varying  in  number  from  one  to  eight. 

If  A  still  be  the  area  of  a  square  in  square  feet,  the  equation  for 
total  volume  in  cubic  yards  is 

V  =  ~^(3*i  +  2Sk  +  8*A».  .  .    SA8). 

118.  The  Prismoidal  Method.  In  Fig.  53  is  shown  a  prismoid, 
which  is  a  solid  having  parallel  bases,  and  which  may  be  composed  of 
any  combination  of  prisms,  cylinders,  pyramids,  cones,  wedges,  or  their 
frustums,  whose  bases  and  apices  lie  in  the  bases  of  the  solid.  But 


\ 

\ 

\ 

\ 

\ 

5         \ 

\ 

5      \ 

4      3 

\ 

/ 

s 

/ 

\ 

j 

\ 

/ 

3     \ 

A 

5     \ 

SI     2 

\ 
\ 

\ 

\ 

\ 
\ 

\ 

\ 

3     \ 

5        N 

6       N 

7      3s, 

s 
\ 

/ 

X 

\ 

/ 

X 

\ 

\ 

1         \ 

A 

c£ 

\ 
2      2\ 

Fig.  52. 


since  the  cylinder  and  cone  are  particular  forms  of  the  prism  and  pyramid  respectively,  and 
since  frustums  may  be  resolved  into  the  simpler  solids,  the  following  is  a  sufficient  definition: 
The  prismoid  is  a  solid  having  parallel  bases,  and  may  be  composed  of  any  combination  of 
prisms,  pyramids,  and  wedges,  whose  bases  and  apices  lie  in  the  bases  of  the  solid.  If  a 
volume-equation  can  be  found  which  is  common  to  these  three  solids,  it  will  be  applicable  to 

their  combination  as  described. 

In  Fig.  53  let  Aj  and  A2  be  the  areas  of 
the  bases  of  the  prismoid,  and  h  the  perpen- 
dicular distance  between  them.  Also  let  A  be 
the  area  of  a  right  section  midway  between  the 
bases.  Then 


Fig.  53. 


+  A2), 


100  SUKFACE  FORMS  AND  EARTHWORK 

which  is  the  prismoidal  formula,  for  it  may  be  shown  that  it  applies  to  each  of  the  elementary 
solids  of  which  the  prismoid  may  be  composed.*  This  formula  is  rigidly  correct  for  all  true 
prismoids.  The  only  approximation  made  in  its  application  to  earthwork  is  in  assuming  that 
the  sides  of  the  figure  are  either  plane  or  warped  surfaces,  while  the  natural  ground  surface 
may  be  quite  otherwise  ;  but  by  taking  h  sufficiently  small  the  figures  may  always  be  made  to 
approach  closely  to  true  prismoids. 

If  the  ground  is  very  uneven,  care  should  be  taken  to  choose  the  positions  of  the  bases  of 
the  prismoids  so  that  the  apices  of  elementary  pyramids  and  the  edges  of  elementary  wedges 
will  lie  in  the  end  bases  of  prismoids  and  not  between  them  ;  otherwise  the  figures  will  not 
closely  approximate  true  prismoids. 

It  should  be  carefully  noted  that  the  area  of  the  middle  base,  Am,  is  not  an  average  of 
the  areas  of  the  end  bases,  but  that  the  lengths  of  its  sides  are  averages  of  the  lengths  of  the 
corresponding  sides  of  the  end  bases.  This  must  be  kept  in  mind  when,  as  is  sometimes 
necessary,  the  value  of  Am  must  be  found  by  interpolating  between  the  known  values  of  Al 
and  A2. 

119.  Consecutive  Prismoids.  In  railway  cuts  and  embankments,  canals,  cuts  and  fills  for 
roads,  etc.,  the  work  is  usually  cross-sectioned  at  regular  intervals,  as  25,  50,  or  100  feet,  thus 
making  a  series  of  prismoids  end  to  end,  the  value  of  h  being  twice  the  distance  between  sec- 
tions. By  reference  to  Fig.  53  it  will  be  seen  that  if  this  were  the  first  of  a  series  of  pris- 
moids, Aj  would  be  used  once,  while  A2  would  be  used  twice  (since  it  is  the  end  of  the  figure 
shown  and  the  beginning  of  the  next  in  succession),  while  Am  belongs  only  to  the  prismoid 

*  This  formula  gives  also  the  volume  of  the  sphere  and  of  the  regular  solids  of  revolution. 


METHODS   APPROXIMATING   THE   PRISMOIDAL   METHOD  101 

shown.     Instead,  therefore,  of  computing  each  prismoid  separately  and  adding  results,   an 
expression  for  the  whole  series  may  be  written, 

V=  Aa  +  4Aa  +  2A3  +  4A4  +  2  A5  +  ...     A».» 


If  the  elementary  volumes  be  odd  in  number,  the  above  equation  will  not  include  the  last 
one,  which  must  be  computed  separately,  either  by  interpolating  Am,  as  described  in  the  last 
article,  and  treating  it  as  a  prismoid,  or  by  one  of  the  methods  of  Art.  121. 

120.  Application  of  Prismoidal  Method  to  Grading.     The  prismoidal  method  may  be  ap- 
plied to  advantage  to  most  of  the  problems  that  arise  as  to  quantities  of  earthwork.     Suppose 
a  hill  to  be  leveled  or  a  depression  to  be  filled;   then  the  areas  included  within  contour  lines 
may  be  made  the  bases  of  prismoids,  and  twice  the  contour  interval  will  be  the  height. 

121.  Methods  Approximating  the  Prismoidal  Method.     For  the  sake  of  simpler  calcula- 
tions one  of  two  assumptions  is  sometimes  made  in  calculating  the  volume  of  the  prismoid,  viz. 

• 

1.  y  ~JL  x  A  !  +  A  2*  which  is  called  the  method  of  average  end  areas. 

—  i  £ 

2.  V  =  -^=n?,   which  is  called  the  method  of  mean  areas. 

If  the  figure  is  a  true  prism,  it  is  evident  that  neither  of  these  equations  involves  any 
approximation  ;  but  in  the  case  of  a  prismoid  the  first  equation  gives  results  too  large,  the 
second  one  gives  results  too  small,  and  the  error  in  the  first  assumption  is  twice  as  great  as 
that  in  the  second. 

*  Twenty-seven  is  here  placed  in  the  denominator  to  give  the  volume  in  cubic  yards. 


102 


SURFACE  FORMS  AND  EARTHWORK 


The  following  may  be 
taken  as  a  general  guide  in 
the  selection  of  the  method :  — 

1.  If  the   end   areas  are 
nearly  alike,  the  meth- 
od    of    average     end 
areas  may  be  used. 

2.  If  the  end  areas  differ 
considerably,  the  meth- 
od  of  mean   areas  or 
the  prismoidal  method 
should  be  used. 

3.  If  the  end   areas  dif- 
fer greatly,   only   the 
prismoidal       methad 
should  be  used. 

122.  Volume  from  a  Con- 
tour Map.  In  Fig.  54  are 
shown  three  series  of  lines 
which,  if  the  student  is  not  skilled  in  reading  contour  lines,  must  be  very  carefully  studied, 
one  series  at  a  time,  till  the  surface  forms  which  they  express  are  clearly  in  mind. 

The  full  lines  are  the  "natural"  contours,  showing  the  natural  or  unimproved  ground 
surface.     Note  that  those  whose  references  are  divisible  by  10  are  heavy  lines  to  aid  the  eye 


Fig.  54. 


VOLUME  FKOM  A  CONTOUK  MAP  103 

in  carrying  the  form  as  a  whole.  The  lines  in  long  dashes  are  contours  showing  what  the  sur- 
face will  be  when  graded.  Both  systems  are  to  be  regarded  as  based  upon  the  same  datum. 

At  a  point  nearly  in  the  middle  of  the  figure,  contour  70  of  the  first  system  crosses  contour 
70  of  the  second  system.  At  this  point  therefore  the  ground  will  be  neither  cut  down  nor 
filled  up  by  the  proposed  grading,  and  it  is  called  a  "grade  point."  Just  above  this  point  is 
one  where  the  72  contours  of  both  systems  cross,  and  this  is  another  grade  point.  There  are 
four  other  similar  points,  and  the  dotted  line  joining  them  is  a  "grade  line."  It  should  be 
noted  carefully  that  this  is  not  a  contour  line,  for  its  lower  end  is  at  an  elevation  10  feet  below 
that  of  its  upper  end.  It  is  simply  a  line  along  which  the  proposed  grading  will  not  necessitate 
either  filling  or  cutting,  but  is  common  to  both  the  present  surface  and  the  proposed  new 
surface.  Another  way  of  stating  the  case  is  that  if  we  were  to  construct  two  profiles  upon 
this  line,  first  using  the  natural  contours,  and  then  using  the  proposed  contours,  the  two 
profiles  would  be  identical. 

At  the  left  of  the  point  to  which  attention  was  first  called  above  is  a  point  where  the  68 
contour  of  the  natural  system  is  crossed  by  the  70  contour  of  the  proposed  system,  which  means 
that  at  this  point  the  ground  is  to  be  made  two  feet  higher  than  it  is  at  present ;  or  as  it  is 
commonly  expressed,  there  is  to  be  a  2-foot  fill.  There  are  four  other  points  at  which  the 
intersecting  contours  denote  a  2-foot  fill,  and  a  dotted  line  is  drawn  through  them  all  and 
marked  F2r.  This  line  is  of  the  same  nature  as  the  grade  line;  it  is  not  a  contour,  but  is 
simply  a  line  at  all  points  of  which  there  is  to  be  a  fill  of  two  feet. 

In  the  same  way  are  constructed  other  lines  showing  successively  increasing  fills  up  to  12 
feet. 

At  the  right  of  the  grade  line  there  are  also  intersections  of  contours  of  the  two  systems, 


104  SURFACE  FORMS  AND  EARTHWORK 

but  in  each  instance  it  is  a  contour  of  the  original  system  which  has  the  greater  reference, 
showing  that  the  ground  is  to  be  cut  away  instead  of  being  filled  up.  By  tracing  out  these 
intersections  the  lines  for  2-foot  cut  and  4-foot  cut  were  drawn. 

'  Referring  to  the  line  of  2-foot  cut,  it  will  be  seen  that  there  are  four  points  at  the  upper 
part  of  the  figure  to  determine  it,  leaving  it  at  k  with  little  indication  as  to  its  further  course. 
The  next  point  which  we  should  look  for  would  be  formed  by  the  crossing  of  contour  70  of  the 
natural  system  and  68  of  the  proposed  system.  But  these  do  not  cross  within  the  limits  of  the 
drawing.  They  could  be  continued  by  guess  to  an  intersection  beyond  the  limits,  and  thus 
furnish  a  point  toward  which  to  draw  the  dotted  line  from  k.  But  such  a  point  would  be  at 
too  great  a  distance  from  k  for  accurately  determining  the  position  of  the  dotted  line  within 
the  limits  of  the  figure.  It  would  help,  however,  to  the  conclusion  that  the  dotted  line  runs 
out  of  the  figure  at  its  right-hand  side,  and  between  contours  70  and  72  of  the  natural  system. 
The  auxiliary  figure  at  the  right  shows  a  method  by  which  a  point  on  the  2-foot-cut  line 
may  be  located  at  the  boundary  of  the  figure.  This  shows,  in  full  line,  a  profile  of  the 
natural  surface,  and  in  broken  line  a  profile  of  the  proposed  surface,  each  taken  along  the 
right-hand  boundary  of  the  main  figure,  and  for  convenience  projected  directly  from  the  points 
where  the  several  contour  lines  reach  it.  Then  by  trial  the  place  is  found  where  these  profiles 
are  two  feet  apart,  vertically,  to  the  scale  used  in  constructing  the  profiles.  This  point  is  at 
ef  in  the  figure,  and  is  shown  projected  to  A,  which  js  the  desired  point  to  which  to  draw  the 
line  of  2-foot  cut.  Any  other  point  in  this  line  between  h  and  k  may  be  found  by  construct- 
ing similar  profiles  on  a  base  passing  through  the  desired  location  of  the  point.  Such  a  base 
might  be  parallel  to  the  boundary  of  the  figure,  but  would  more  naturally  be  taken  so  as  to  be 
about  normal  to  the  contour  lines  which  it  would  cross. 


VOLUME  FROM  A  CONTOUR  MAP  105 

The  volume  of  cut  and  fill  may  now  be  estimated  by  either  one  of  the  three  following 
methods :  — 

1.  With  a  planimeter  measure  the  area  bounded  by  the  grade  line,  the  F2'  line,  and 
the  top  and  bottom  limits  of  the  figure.     Multiply  this  area  by  1,  which  is  the  average  fill  in 
feet  over  the  area.     Measure  the  area  bounded  by  F2',  F4',  and  the  limits  of  the  figure,  and 
multiply  it  by  3,  which  is  the  average  fill  over  this  area.     Proceed  in  the  same  way  with  all 
the  similar  areas  which  are  in  fill,  and  add  the  results  for  the  total  volume  of  fill  in  cubic  feet. 
Obtain  the  volume  of  cut  in  the  same  way. 

In  many  cases  areas  will  be  of  irregular  shapes,  and  it  will  be  evident,  for  instance,  that 
more  than  half  of  a  given  area  is  subject  to  a  fill  greater  than  the  average  of  the  fill  at  its 
edges.  In  such  a  case  judgment  must  be  used  as  to  the  exact  quantity  by  which  the  area  is  to 
be  multiplied. 

2.  With  a  planimeter  determine  the  area  included  by  the  grade    line  and  the  limits  of 
the   figure  at  its  left.      Measure  also  the  similar  areas  determined  by  lines  F2'  and  F4'  re- 
spectively.    These  three  areas  may  now  be  taken  as  the  three  bases  of  a  prismoid  whose  height 
is  the  united  heights  of  the  two  layers  of  fill  thus  involved ;  that  is,  in  this  case,  four  feet. 
Other  successive  prismoids  may  be  formed  in  the  same  way,  both  for  the  remaining  fill  and  for 
the  cuts. 

3.  The  entire  area  may  be  divided  into  squares  or  rectangles,  each  of  which  will  be  the 
base  of  an  elementary  prism  of  cut  or  fill.      One  square  of  such  a  series  is  shown  at  ABCD. 
By  inspecting    the    position  of    its    corners  with   reference   to   the    adjacent  fill  lines,    the 
depth  of  fill  at  each  corner  (that  is,  the  height  of  each  edge  of  the  prism)  may  be  rather 
closely  estimated,  and  the  volume  may  be  found  as  explained  in  Art.  116. 


106  SUKFACE  FORMS  AND  EARTHWORK 

It  is  evident  that  some  prisms  will  be  partly  in  fill  and  partly  in  cut.  In  this  case  the 
algebraic  sum  of  corner  heights  may  be  taken,  or  the  prism  may  be  divided  into  two  irregular 
ones  at  the  grade  line,  and  each  taken  separately. 

In  practice  a  set  of  contours  such  as  the  proposed  contours  of  Fig,  54  may  not  disappear 
at  the  limits  of  the  drawing,  where  they  would  seem  to  be  conveniently  disposed  of.  If  there 
are  summits  or  depressions  without  outlets,  some  of  the  contours  will  close  upon  themselves; 
otherwise  they  must  ultimately  run  into  and  be  merged  with  the  natural  contours  of  the  same 
reference  numbers,  since  no  grading  operations  are  of  unlimited  extent. 

123.  Treatment  of  the  Plan.  The  systems  of  lines  shown  in  Fig.  54  may  be  brought  out 
in  various  ways  according  to  the  exact  purposes  of  the  plan,  and  with  reference  to  the  degree 
of  skill  possessed  by  those  who  will  examine  it. 

The  natural  contours  may  be  shown  in  full  lines,  either  black  or  burnt  sienna,  while  the 
proposed  contours  may  be  broken  lines  in  black  or  full  lines  in  some  color.  The  lines  of 
cuts  and  fills  may  be  dotted  lines  in  black  or  full  lines  in  still  another  color.  If  the  plan 
is  to  be  examined  by  one  unskilled  in  reading  such  drawings,  it  is  best  to  use  colors  rather 
freely. 

If  the  plan  is  to  serve  as  a  construction  plan  for  work  already  decided  upon,  the  new 
contours  are  best  drawn  in  full  lines,  while  the  natural  ones  are  dotted,  and  the  lines  of  cuts 
and  fills,  if  shown  at  all,  in  some  color. 

A  very  good  plan,  when  much  work  is  to  be  done  upon  such  an  area,  is  to  make  one  trac- 
ing showing  the  natural,  and  another  showing  the  proposed,  contours.  The  two  tracings  may 
then  be  used  separately  to  obtain  prints;  or,  by  superposing  one  exactly  upon  the  other,  a  print 


BALANCING  CUTS  AND  FILLS  107 

may  be  made  showing  both  sets  of  contours,  which  may  then  be  used  for  calculations  of  volume, 
for  comparison  of  the  two  surfaces,  etc. 

It  is  sometimes  of  interest  to  use  different  tints  to  distinguish  the  areas  in  cut  from  those 
in  fill ;  or  one  of  these  areas  may  be  cross  hatched  for  the  same  purpose. 

124.  Balancing  Cuts  and  Fills.  If  excavation  is  in  excess  of  fill,  the  surplus  earth  must 
be  deposited  in  a  spoil  bank,  often  at  a  distance  from  the  work ;  if  the  fill  exceeds  the  cut,  ma- 
terial must  be  obtained  from  a  borrow  pit,  which  involves  expense  both  for  material  and  trans- 
portation. 

It  is  therefore  desirable,  whenever  possible,  to  design  the  work  so  that  the  material  ex- 
cavated will  be  sufficient  to  make  the  fills  ;  also  that  the  cuts  and  the  equivalent  fills  be  not 
far  separated,  for  if  surplus  earth  has  to  be  carried  more  than  a  certain  distance  (often  stipu- 
lated as  500  feet  in  contract  work),  an  extra  charge  is  made  for  the  overhaul.  The  balancing 
of  cuts  and  fills,  as  it  is  called,  is  done  on  the  profile  for  such  work  as  highway  and  railroad 
construction,  where  the  area  covered  is  long  and  narrow.  The  surface  usually  may  be  as- 
sumed as  approximately  level  transversely  to  the  profile,  so  that  if  the  proposed  new  surface 
line  be  kept  above  the  profile  of  the  natural  surface  in  some  places  by  about  the  same  amount 
that  it  passes  below  it  in  others,  the  volumes  in  cut  and  fill  will  approximately  balance.* 

A  trial  surface  line  is  usually  found  by  holding  a  thread  taut  and  placing  it  in  various 
positions  on  the  profile  until  one  is  found  that  satisfies  the  eye  as  to  equivalence  of  cuts  and 
fills.  This  position  is  then  drawn  in  pencil  and  the  volumes  calculated. 

*  The  cuts  must  be  somewhat  in  excess  of  fills  to  allow  for  the  fact  that  earth  shrinks  when  deposited  in  embank- 
ment. 


108  SURFACE  FORMS  AND  EARTHWORK 

In  grading  over  an  extended  area  a  contour  plan  such  as  that  shown  in  Fig.  54  is  the  best 
means  for  studying  the  cuts  and  fills.  Starting  with  the  natural  contours,  a  trial  set  of  new 
contours  may  be  sketched  on  rather  roughly.  Then  it  will  be  seen  by  inspection  whether  the 
cuts  and  fills  approximately  balance.  In  the  figure  it  is  evident  that  the  fill  is  largely  in  excess 
of  the  cut,  not  only  because  the  area  covered  by  it  is  greater,  but  also  because  the  required 
depth  is  greater.  A  nearer  approach  to  a  balance  may  be  made  by  simply  renumbering  the 
proposed  contours.  If,  for  instance,  each  be  marked  two  units  less,  the  grade  line  will  be 
thrown  to  the  position  now  occupied  by  F2',  thus  making  the  area  in  cut  somewhat  greater 
than  that  in  fill  ;  moreover,  the  greatest  fill  will  be  reduced  to  10  feet,  while  the  greatest  cut 
will  be  increased  to  6  feet.  If  a  slightly  greater  cut  and  a  slightly  smaller  fill  be  found  desir- 
able, then  some  or  all  of  the  proposed  contours  will  be  moved  toward  the  top  of  the  figure. 

125.  Problems.  The  contour  map  whose  construction  is  required  in  Problem  1  is  the 
basis  for  the  subsequent  problems.  Problems  2,  3,  and  4  may  be  worked  out  on  one  sheet 
without  overlapping,  and  the  same  is  true  of  Problems  5  and  6.  Problem  7  requires  a 
whole  sheet. 

The  most  satisfactory  way  of  solving  the  problems  is  to  work  each  group  on  a  sheet  of 
tracing  cloth  fastened  over  the  contour  map.  It  will  then  be  easy  to  omit  parts  of  original 
contours  covered  up  or  cut  out  by  the  structures  under  consideration. 

1.  To  a  scale  of  1  inch  =  50  feet  draw  coordinate  lines  800  E.  to  1500  E.,  each  inclusive, 
and  500  S.  to  1000  S.,  each  inclusive,  as  shown  on  Plate  V.  These  should  be  inked  and  num- 
bered at  once  in  red,  the  lines  being  made  very  fine.  Draw  in  pencil  an  intermediate  set  of 
coordinates,  thus  dividing  the  whole  area  into  50-foot  squares.  The  corner  heights  are  not 


Plate  V. 


5005 


600  S 


7005 


8005 


9005 


/OOOS 


51.0             55.0 

55.2           '56.3 

54.0           49.8 

46.6          148.0 

49.7             51.2 

50.9            151.1 

49.4           |46.5   43.4 

£7.8         ,49.6 

JI.Z        _|S2.6       . 

49.8        _|45.Z        _ 

42.6         ,44.4 

47.1         _(48.f 

48.0       _|45.7 

44.6        ,42.1    39.8 

44.6          44.8 

45.0           46.5 

43.2           40.1 

38.4            39.8 

41.0            40.8 

40.0           J9.6 

39.1            38.0     369 

40.4        ,58.7 

J8.6         |36.4 

33.8        _J_33.0       _ 

32.8       _|33.I 

53.6           ,34.3 

T- 

14.6        _|35.l 

J5.0          |34.2  35.3 

36.5           34.3 

32.0           31.8 

33.2           34.Z 

33.6           35.4 

32.2           31.5 

31.9           ,31.6 

31.5            31.5     31.6 

3E.7          |3!.8 

34.5         ,39.1 
"T 

42.0       _i4Z.5 

41.3          ,39.0 

~T 

36.0         ,31.8 
T 

1 

35.3         ,36.0 
+ 

35.2        _(34.8    35.5 

31.8          |35.l 

40.7           44.9 

48.0          50.  2 

49.0          41.8 

36.6           35.4 

41.0           43.0 

40.6         ,40.5   404 

1 

33.0         I37.Z 

42.5         ,45.8 
T 

47.9       ^52.0       . 

^54.0      _i_40.l 

40.5         ,45.0 
T 

5Z.I       _|53.3      , 

48.8      _i47.4  46.0 

35.4          35.2 

38.2           40.1 

41.  2            41.6 

41.2           43.6 

47.6          52.4 

59.0            59.  Z 

55.7           53.3  51.4 

30.4         133.0 

34.3        ,36.? 

+ 

38.1        _|4I.6 

45.0         ,48.5 
T 

52.0         ,56.6 

-f-             - 

62.  0         ,64.8 

6Z.S         |58.Z    556 

3Z.O         I33.Z 

36.1           140.0 

42.6         |45.0 

47.7           |50.7 

53.8          |58.4 

63.0          |68.0 

68.5          166.4    61.0 

PROBLEMS  111 

to  be  copied  on  the  drawing,  but  used  directly  from  the  plate,  and  the  intermediate  coordinate 
lines  are  to  be  erased  as  soon  as  the  contours  are  drawn. 

By  the  use  of  the  corner  elevations  construct  profiles  on  the  north  and  south  lines  (the 
reason  will  appear  when  the  contours  are  drawn),  and  from  these,  as  explained  in  Art.  Ill,  find 
contour  points  from  which  2-foot  contour  lines  are  to  be  drawn.*  The  profiles  should  be  made 
on  profile  paper.  A  vertical  scale  of  1  inch  =  8  feet  is  suitable.  Show  the  contours  and  their 
references  in  B.S.,  and  use  a  heavy  line  for  each  contour  whose  reference  is  divisible  by  ten. 

2.  On  line  900  E.  as  a  center  line,  a  cut  extending  the  entire  width  of  the  map  is  to  be 
made  under  the  following  requirements:   bottom  width  25  feet;  elevation  of  bottom  30.0; 
side  slopes  1^  :  1.     On  a  scale  of  1  inch  =  10  feet  draw  cross-sections  at  every  50  feet  along 
the  center  line,  showing  the  original  surface  and  the  required  cut.     From  the  planimetered 
areas  of  the  cross-sections  find  the  volume  of  the  cut  by  the  prismoidal  formula.     By  the  use 
of  the  proper  points  taken  from  the  cross-sections,  draw  on  the  map,  in  full  black  lines,  the 
intersections  between  the  side  slopes  and'  the  natural  surface.     Draw  the  foot  of  each  slope  in 
black,  and  rule  the  contours  on  the  slopes  in  B.S.,  but  do  not  draw  any  of  the  latter  till  the 
top  of  the  slope  has  been  drawn  as  above  described. 

3.  The  rectangle  bounded  by  500  S.,  1000  S.,  1200  E.,  and  1500  E.,  is  to  be  graded  to  a 
plane  surface  described  as  follows :  at  point  1000  S.,  1200  E.,  its  elevation  is  to  be  38.0 ;  it  is 
to  be  level  along  all  lines  running  northeast  and  southwest ;  and  it  is  to  have  a  grade  of  3  % 

*  The  teacher  may  find  it  advisable,  as  a  means  of  saving  time,  to  distribute  the  making  of  the  several  profiles 
among  members  of  the  class,  and  then  to  allow  an  exchange  of  tick  strips.  A  further  division  of  labor  may  be  made  by 
allowing  some  students  to  read  elevations  while  others  plot  them.  But  each  student  should  interpret  for  himself  the 
contour  points  obtained. 


112  SURFACE  FOEMS   AND  EARTHWORK 

running  downward  to  the  northwest.  Draw  2-foot  contours  in  black  to  express  this  surface, 
the  natural  contours  being  in  B.S.  Draw  grade  lines  in  dotted  black,  lines  of  fill  in  blue,  and 
lines  of  cut  in  red.  Find  the  volumes  of  cut  and  fill,  (a)  by  the  prismoidal  method,  (5)  by 
method  (1)  of  Art.  122. 

4.  The  strip  between  lines  1000  E.  and  1100  E.  is  to  be  graded  to  a  surface  conforming 
to  the  following  description :  beginning  at  1000  S.  it  is  to  slope  upward  toward  the  north  3  % 
for  the  first  200  feet ;  thence  100  feet  level ;  thence  for  100  feet  4  %  downward ;  thence  for 
100  feet  6%  upward.     Express  these  surfaces  by  2-foot  contours  in  B.S.,  so  placed  that  the 
cuts  will  approximately  balance  the  fills.     Divide  the  area  by  blue  lines  into  squares  of  50  feet 
on  each  side,  and  calculate  the  quantities  of  cuts  and  fills  by  method  (3)  of  Art.  122.     (Sug- 
gestion :  construct  a  profile  of  the  natural  surface  along  the  center  line  of  the  strip,  and,  on 
tracing  paper  or  cloth,  construct  also  the  profile  of  the  required  surface  without  regard  to 
actual  elevations.     Lay  the  second  profile  over  the  first,  and  in  such  relation  to  it  that  a  bal- 
ance of  cuts  and  fills  seems  to  be  secured.     The  positions  and  references  of  contours  to  ex- 
press the  required  surface  may  now  be  determined.) 

5.  The  square  bounded  by  lines  500  S.,  800  S.,  800  E.,  and  1100  E.,  is  a  borrow  pit. 
Successive  layers  of  earth  are  taken  out,  the  surface  of  the  excavated  area  being  left  level  in 
each  case.     These  layers  extend  respectively  to  elevations  52,  44,  36,  and  28.     The  sides  of  the 
excavation  are  on  a  slope  of  1|  to  1,  and  the  tops  of  the  slopes  follow  the  boundary  of  the 
square.     Find  the  volume  of  each  of  the  four  layers.     (Each  of  the  three  upper  layers  is  in 
two  parts,  but  is  called  one  layer.)     Use  black  lines  to  show  the  upper  layer,  blue  for  the  sec- 
ond, red  for  the  third,  and  green  for  the  bottom.     Colored  lines  may  be  drawn  close  to  con- 
tours when  these  form  parts  of  boundaries. 


PROBLEMS  113 

This  is  the  kind  of  problem  on  which  much  time  may  be  spent  in  applying  a  refinement 
of  method  for  computing  quantities.  When  the  conditions  do  not  lend  themselves  readily  to 
the  application  of  a  theoretically  exact  method,  it  is  often  better  to  apply  with  judgment  an 
approximate  formula  to  large  volumes  rather  than  to  cut  such  volumes  up  into  smaller  ones 
which  may  be  computed  by  the  prismoidal  formula,  for  instance.  In  the  present  case  it 
will  be  noted  that  portions  of  layers  are  of  uniform  thickness,  but  of  unequal  top  and  bottom 
areas;  while  other  portions  are  of  unequal  thickness  as  well.  It  is  suggested  that  each  layer 
or  independent  section  of  a  layer  be  divided  into  two  parts,  for  one  of  which  an  average  base 
shall  be  chosen,  and  for  the  other  both  a  proper  base  and  thickness  shall  be  chosen  for  comput- 
ing volumes. 

6.  The  center  line  of  a  highway  starts  at  point  1000  S.,  1200  E,,  and  runs  due  north  200 
.feet,  where  it  turns  to  the  right  by  an  arc  of  100  feet  radius,  and  continues  due  northeast  to  the 

edge  of  the  map.  The  roadway  is  to  be  50  feet  wide,  and  for  simplicity  is  to  be  considered 
level  transversely.  At  the  point  of  beginning  its  elevation  is  50.0.  It  has  a  downward  slope 
of  4%  to  the  beginning  of  the  curve,  from  which  point  it  is  level.  The  side  slopes  are  2  :  1 
for  both  cut  and  fill.  By  means  of  2-foot  contours  alone  work  out  the  lines  showing  the  tops 
and  toes  of  the  slopes.  Calculate  the  length  of  the  roadway  (measured  horizontally)  on  its 
center  line,  and,  calling  the  point  of  beginning  Sta.  0  +  0,  write  the  stations  on  the  center  line, 
including  the  pluses  at  the  end  of  the  curve  and  at  the  upper  border  of  the  map.  Draw  the 
center  line  and  the  tops  and  toes  of  slopes  in  black,  but  use  B.S.  for  slope  contours. 

7.  A  rectangular  reservoir  has  a  flat,  level  top  25  feet  wide  and  at  EL  48.0.     The  outside 
corners  are  at  points  600  S.,  900  E. ;  600  S.,  1400  E. ;  900  S.,  900  E. ;  and  900  S.,  1400  E.     The 
outside  slopes  are  3:1,  and  the  inside  slopes  are  1 :1.     The  bottom  is  flat,  and  at  El.  6.0.     By 


114  SURFACE  FOEMS  AND  EARTHWORK 

means  of  contours  only  find  the  tops  and  toes  of  all  slopes.  Compute  the  volumes  of  cuts  and 
fills  by  such  method  or  methods  as  seem  best  adapted.  Ink  in  blue  the  contours  relating  to 
fills,  and  in  red  those  relating  to  cuts,  using  black  where  coutour  lines  are  also  the  tops  or 
toes  of  slopes.  Use  2-foot  contours  for  the  outside  slopes,  and  6-foot  contours  for  the  inside 
slopes. 


CHAPTER   VII 

CONVENTIONAL   TREATMENT  FOR   SURFACES   AND   SECTIONS 

126.  Reasons  for  Treatment.     The   present  chapter  has  reference   to   the   treatment   of 
materials  employed  in  building  structures  which  rest  directly  upon  the  earth,  and  also  of  the 
natural  earths,  rock,  and  water.     It  is  outside  the  scope  of  this  work  to  speak  of  the  conven- 
tional treatment  of  metals  and  some  other  materials  of  engineering. 

A  drawing  may  serve  its  purpose  if  it  shows  only  outlines  of  figures  and  divisions  between 
different  materials.  But  if  proper  and  suggestive  conventional  treatment  or  "  rendering  "  be 
used  to  indicate  different  materials,  especially  on  sections,  the  drawing  is  much  more  easily 
read,  and  is  therefore  more  useful,  as  well  as  more  attractive,  and  hence  more  satisfactory.  By 
the  use  of  appropriate  conventional  signs  it  is  possible  to  avoid  many  notes  on  the  drawing 
which  otherwise  would  be  required  to  explain  the  nature  of,  and  the  relations  between,  the 
various  materials.  Again,  the  use  of  conventions  enables  the  engineer  to  express  shades  of 
quality  of  construction  work  ;  for  instance,  in  uncoursed  rubble,  the  quality  of  work  as  to  the 
fitting  of  stones  may  be  expressed  rather  more  clearly  than  in  written  specifications. 

127.  Materials  in  Elevation,  Plate  VI.     The  term  rendering  is  applied  to  the  treatment 
of  materials  in  elevation  or  plan  to  indicate  the  nature  of  the  materials,  or  the  form  of  the 
objects,  or  both.     The  nature  of  materials  is  brought  out  by  more  or  less  suggestive  conven- 
tions, and  forms  are  expressed  by  shades  and  shadows. 

116 


116  CONVENTIONAL  TREATMENT  FOR   SURFACES   AND   SECTIONS 

The  conventional  treatment  for  the  most  commonly  used  materials  is  as  described  below, 
and  shown  on  the  plate. 

1.  Hammered-face  Stone.     After  the  joints  are  drawn  pencil  lines  are  ruled  parallel  with 
and  near  the  left-hand  and  upper  edge  of  each  stone,  and  the  spaces  between  these  and  the  joints 
are  left  blank  to  give  relief  to  the  work,  and  to  suggest  the  "  draft "  which  is  often  cut  around 
the  face.     The  sets  of  short  vertical  lines  are  then  drawn  with  a  fine  pen.     Regularity  of  order 
among  these  sets  of  lines  is  to  be  avoided.     Fine  dots  are  then  added  to  fill  up  the  larger  blank 
spaces  and  to  clearly  define  the  draft  lines.     By  using  very  fine  lines  and  dots  a  delicacy  of 
treatment  may  be  given  which  it  is  not  easy  to  show  in  an  engraved  plate. 

2.  Rock-face  Stone.     The  edges  of  the  stones  of  this  class  are  usually  "  pitched  "  to  a 
straight  line.     This  line  is  suggested  by  leaving  a  narrow  blank  area  at  the  top  and  left-hand 
of  each  stone.     The  bottom  and  right-hand  edge  of  each  stone  is  then  finished  in  a  heavy  and 
quite  irregular  shadow  line.     Next  are  drawn  the  heavy  shadow  lines  on  the  faces  of  the  stones 
to  define  the  edges  of  projecting  portions.     Areas  of  medium  dark  tone  are  next  shown  by  sets 
of  parallel  lines,  and  a  few  dots  are  added  last  of  all.     Considerable  practice  may  be   found 
necessary  to  avoid  an  unpleasing  monotony  in  showing  this  face.     It  will  be  found  very  help- 
ful to  study  an  existing  rock-face  wall,  making  pencil  sketches  of  individual  stones. 

3.  Split-face  Stone.     The  rendering  consists  simply  of  groups  of  vertical  lines.      Some 
variety  should  be  sought  in  the  grouping  of  these,  and  the  upper  and  left-hand  edges  of  the 
stones  should  be  avoided. 

4.  Uncoursed  Rubble.     The  outlining  of  individual  stones  should  have  reference  to  the 
sizes  of  stones,  the  allowable  thickness  of  joints,  and  the  allowable  departure  of  bed  joints  from 
a  horizontal  line.     If  spalls  are  to  be  used  to  fill  the  larger  joint  spaces  they  are  to  be  outlined, 


iii'-;».-iiii:'7.-,;rii;:ir,v"irJ,- 'in""";  iivi" ". 

^^i^*:»*»:H5i*i 

ii.^']  ^•'•.lyA?..-. '«••:.;•  !H.>.N': 


Hammered -face 
Stone 


Uncoursed  Rubble 


r      i 


i        i 


i    .    i       r 


I        I 


Brickwork 


Rock-face  Stone 

(Ashlar  Masonry) 


Riprap 


Wood 

Edge  and  Side  of  Timber 


Split-face  Stone 

(Coursed  Rubble) 


Broken  Stone 


Wood 

End  of  Timber 


Plate  VI. 

117 


MATEEIALS  IN  ELEVATION  119 

and  the  remaining  portions  of  the  joints  are  then  to  be  made  solid  black.  If  it  is  desirable  to 
distinguish  between  dry  rubble  and  rubble  laid  in  mortar,  the  solid  black  joints  may  be  used 
for  the  dry  work,  while  dots  placed  thickly  in  the  joint  spaces  may  indicate  mortar. 

5.  Riprap.    The  drawing  should  show  the  sizes  of  stones  allowed  by  the  specifications,  and 
should  also  indicate  the  quality  of  work  as  to  the  relative  positions  of  stones.     If  the  stones 
are  to  be  dumped  in  place,  the  drawing  should  show  them  placed  without  regularity;  if  they 
are  to  be  placed  by  hand,  some  regularity  of  arrangement  should  be  shown,  as  in  uncoursed 
rubble. 

6.  Broken  Stone.     Sketchy  and  rather  widely  separated  suggestions  of  irregular  pieces  of 
stone,  with  a  few  dots  in  the  larger  open  spaces,  form  this  convention.     The  lower  and  right- 
hand  edges  of  the  stones  should  be  drawn  with  a  little  heavier  pen  stroke  than  is  given  to  the 
other  edges.     It  will  usually  be  necessary  to  draw  individual  stones  much  larger  than  they 
would  actually  be  to  the  scale  of  the  drawing. 

7.  Brickwork   is  shown  by  simply  indicating  the  joints.     In  order  that  the  treatment  be 
suggestive  the  individual  bricks  must  be  drawn  to  scale,  and  this  becomes  very  laborious 
when  the  scale  of  the  drawing  is  small.     Hence  it  is  not  uncommon  to  use  no  convention  at 
all  for  brickwork,  the  outlines  only  of  the  structure  being  shown.     It  is  often  quite  suffi- 
cient, and  even  preferable,  to  show  the  convention  on  portions  only  of  the  whole  area  of  brick- 
work.    The  limits  and  character  of  the  work  can  thus  be  shown  with  comparatively  little 
labor. 

8.  Wood.     There  are  two  characteristics  common  to  most  kinds  of  timber,  which  suggest 
the  methods  of  showing  it  on  drawings.     First,  all  woods  grow  by  the  addition  of  yearly  layers 
extending  around  the  trunk.     There  are  visible  lines  separating  these  layers,  and  they  are 


120  CONVENTIONAL   TREATMENT  FOR   SURFACES   AND  SECTIONS 

called  annular  rings.  These  furnish  the  concentric  curves  by  which  the  end  of  the  timber  is 
most  suggestively  shown.  Secondly,  many  trees,  notably  the  oaks,  have  thin  plates  of  close- 
grained  material  called  medullary  rays  arranged  radially,  and  therefore  cutting  the  annular 
rings  normally.  When  a  log  is  cut  into  timber,  the  saw-cut  intersects  the  rings  and  rays  in 
ever-changing  lines  and  figures.  To  indicate  the  characteristics  of  the  different  varieties  of 
wood  by  showing  the  figures  furnished  by  the  medullary  rays  would  involve  too  much  labor, 
and  it  is  customary  to  consider  only  the  lines  furnished  by  the  rings,  except  that  in  showing 
the  end  of  timber  the  rays  are  drawn.  The  edge  of  timber  (and  especially  of  boards  and 
planks)  is  shown  by  somewhat  wavy  lines  not  joining  each  other,  and  not  closing  upon  them- 
selves, while  the  side  is  shown  with  more  variety  of  marking.  Observation  of  the  lines  on 
unfinished  timber  will  be  useful  in  giving  hints  as  to  variety  of  markings. 

128.  Materials  in  Section,  Plate  VII.  The  nature  of  materials  is  universally  indicated  on 
cross-sections  of  structures,  and  very  commonly  on  profiles. 

In  several  cases  the  conventions  on  this  plate  contain  section  lining,  and  directions  are 
given  as  to  the  spacing  of  the  lines.  Thus  for  brickwork  the  spacing  is  "  2  at  42°."  This 
assumes  that  the  Both  section  liner  (Art.  10)  will  be  used,  in  which  case  the  pawl  is  to  be 
arranged  to  pass  two  notches  on  the  bar,  and  the  ruling  arm  is  to  be  set  at  42°  on  the  arc.  The 
whole  instrument  should  then  be  turned  so  that  the  ruling  arm  will  be  at  45°  with  the  lower 
border  of  the  drawing.  In  the  plate  all  section  lines  are  shown  running  upward  to  the  right. 
In  practice,  however,  if  there  are  adjacent  areas  to  be  cross-sectioned,  the  alternate  ones  should 
have  the  lines  running  upward  to  the  left,  whether  or  not  the  material  in  the  adjacent  areas 
is  the  same. 


'»•.•«'•  »•"•»•  ;»•.  c.'».'p'-«  ;  13  •.  <j'.  x>  '»i.Vo« 

--V"  Expanded  Metal  >«a 

\^!->iv'^v.':y^':^^';f^ 


Brickwork 
2  at  4z° 


Cut  Stone 

I  at  84° 


Concrete 


Reenforced  Concrete 


Coursed  Rubble 

2  at  45° 


Uncoursed  Rubble 
2  at  45° 


Riprap 

2  at  45J 


Broken  Stone 


Natural  Rock 


Plate  VII. 

121 


MATERIALS   IN   SECTION  123 

The  spacings  given  are  suitable  for  moderately  large  areas  and  ordinary  working  scales. 
If  the  areas  to  be  section-lined  are  very  small,  the  lines  should  be  drawn  closer  together. 

1.  Brickwork  is  shown  by  simple  lining  as  indicated.     If  the  scale  is  large,  the  joint  lines 
between  individual  bricks  may  also  be  shown. 

2.  Concrete.     The  area  is  first  covered  with  triangular  markings  to  represent  broken  stone, 
the  right-hand  and  lower   sides   being   shaded,  and  care  being  taken  that  the  bases  of  the 
triangles  are  not  all  parallel,  but  rather  arranged  in  a  variety  of  positions.     The  remainder  of 
the  surface  is  then  covered  with  dots  to  represent  sand  and  cement. 

3.  Reenforced  Concrete.     The  concrete  itself  is  represented  as  described  above,  except  that 
near  the  reinforcement  the  triangles  are  made  small  and  sketchy. 

Expanded  metal  is  shown  by  short  lines  drawn  at  30°  with  the  horizontal,  the  lower  end 
of  each  line  being  slightly  to  the  right  of  a  vertical  through  the  upper  end  of  the  preceding 
line. 

Steel  bars  are  shown  in  elevation  or  section  as  the  case  may  require,  and  may  be  either 
round  or  square,  according  to  the  choice  of  bar. 

4.  Cut  Stone.     In  general  the  joints  in  a  cross-section  will  not  be  as  close  as  shown  in  the 
figure  except  for  a  short  distance  back  of  the  face.     The  whole  is  section-lined  as  shown. 

5.  Coursed  Rubble.     The  arrangement  of   joints  is  to  be  made  in  accordance  with  the 
quality  of  work  contemplated,  and  the  surface  section-lined  as  shown. 

6.  Uncoursed  Rubble  is  like  the  same  work  in  elevation  with  the  addition  of  the  section 
lines. 

7.  Riprap  is  shown  as  in  elevation  except  that  section  lines  are  added. 

8.  Broken  Stone.      Individual  stones  are  fully  outlined  and  placed  close  together.     To 


124  CONVENTIONAL  TEEATMENT  FOR  SUEFACES  AND   SECTIONS 

avoid  placing  them  in  rows  it  is  well  first  to  cover  the  area  with  stones  placed  far  apart,  and 
then  gradually  fill  up  the  spaces  with  other  stones. 

9.  Natural  Rock.  First  draw  the  long  lines  which  are  nearly  vertical,  and  slightly 
crooked  and  tapering.  Then  draw  the  second  set  of  lines  between  these,  and  finally  the  sets 
of  fine  parallel  lines  having  a  variety  of  directions. 

129.    Materials  in  Section  (continued),  Plate  VIII. 

1.  Natural  Earth.     First  work  across  the  top  of  the  area,  putting  in  the  sets  of  short 
parallel  lines  extending,  for  instance,  downward  to  the  left.     Then  go  over  the  same  ground 
again,  putting  in  the  sets  extending  downward  to  the  right,  and  finally  the  horizontal  lines. 
In  the  same  way  treat  another  narrow  strip  below  the  first,  and  so  continue  till  as  much  space 
is  treated  as  is  desired,  gradually  making  the  lines  finer  and  farther  apart. 

2.  Earth  Filling.     It  is  best  to  start  with  sets  of  lines  having  a  certain  direction,  and  to 
scatter   the   groups   widely  over   the   area.     Then   draw   scattering   groups   having  another 
direction,  and  thus  gradually  cover  the  area,  being  careful  that  wide  spaces  to  be  filled  with 
dots  are  left  between  adjacent  groups.     Variety  should  be  sought  in  making  lines  of  varying 
length  and  number  in  the  groups,  and  by  making  some  lines  slightly  more  crooked  than  others. 

3.  Filling  in  Layers.      Draw  first  the  long,  broken,  and  moderately  heavy  lines  whose 
distances  apart  are  to  express  the  thickness  of  the  layers.     Then  follow  with  the  closed  figures 
representing  gravel,  the  short  fine  dashes,  and  finally  the  dots. 

4.  Clay  is  expressed  by  lines  of  short  dashes  at  45°  with  the  horizontal.     In  starting  the 
lines  care  should  be  taken  that  the  first  dashes  in  the  various  lines  shall  not  be  of  the  same  length, 
also  that  variety  be  made  in  the  length  of  the  dashes  in  each  line,  otherwise  many  breaks  between 


Natural  Earth 


Clay 


Mud 


Earth  Filling 


Clay  Puddle 


Gravel        Sand 


Filling  in  Layers 


Loam 


Water 


Plate  VIII. 

125 


MATERIALS   IN   SECTION  127 

dashes  in  successive  lines  will  come  opposite  one  another,  giving  an  undesirable  appearance  of 
white  lines  crossing  the  area. 

5.  Clay  Puddle.     This  is  like  the  above,  except  that  the  lines  of  dashes  are  horizontal. 
The  same  caution  must  be  observed  concerning  rows  of  breaks  between  dashes. 

6.  Loam.     Loam  is  most  commonly  deposited  as  a  layer  above  other  filling.     In  this  case, 
and  also  when  a  natural  layer  is  to  be  indicated,  the  depth  of  the  layer  is  defined  in  pencil,  to 
scale,  and  the  space  is  then  filled  with  rather  heavy  vertical  lines  with  spaces  between  only 
slightly  greater  than  the  thickness  of  the  lines.     The  latter  should  be  slightly  wavy,  and  the 
undulations  in  one  line  should  correspond  in  position  with  those  in  the  preceding  line. 

Occasionally  loam  is  deposited  in  a  mass  rather  than  in  a  layer,  in  which  case  other  series 
of  lines  are  drawn  below  the  first.  The  ends  of  these,  however,  need  not  define  a  horizontal 
line,  but  may  define  diagonal  and  curved  lines  as  shown  at  the  left  of  the  figure  ;  then  if  the 
ends  of  lines  in  adjacent  groups  are  not  brought  quite  together,  there  will  be  an  appearance  of 
irregular  white  lines  running  through  the  area. 

If  it  is  desired  to  show  an  indefinite  depth,  the  lines  are  tapered  downward  as  shown  at  the 
middle  of  the  figure. 

7.  Mud.     This  convention  is  the  same  as  that  for  loam  except  that  the  lines  are.  heavier, 
farther  apart,  and  drawn  at  45°  with  the  horizontal. 

8.  Gravel  is   shown  by  first  covering  the  area  with  small  closed  figures  approximately 
circular  in  form,  and  shaded  on  the  lower  right-hand  side  ;  these  represent  the  larger  stones, 
and  should  be  distributed  at  random.     The  smaller  stones  and  sand  are  represented  by  dots 
evenly  distributed  among  the  closed  figures. 

Sand  is  shown  by  dots  evenly  distributed  and  placed  at  random  so  as  not  to  suggest  ar- 


128  CONVENTIONAL  TREATMENT   FOR   SURFACES   AND   SECTIONS 

rangement  in  lines.  The  sizes  of  the  dots  may  be  varied  to  indicate  different  degrees  of  fine- 
ness of  the  sand.  This  should  be  done  by  using  coarser  or  finer  pens,  and  not  by  differing 
pressures  on  the  pen.  In  order  to  make  the  dots  rapidly,  and  yet  keep  them  dots,  rather  than 
short  dashes  or  tapered  strokes,  the  following  precautions  should  be  observed  :  hold  the  pen  at 
a  large  angle  with  the  paper  —  about  65°  ;  move  the  pen  vertically  up  and  down  so  as  to 
strike  the  paper  squarely  ;  touch  the  paper  so  lightly  that  the  nibs  of  the  pen  will  not  be 
spread. 

9.  Water.     The  surface  is  shown  by  a  heavy  line,  and  as  the  work  proceeds  downward 
the  lines  are  made  lighter  and  farther  apart.     The  last  few  lines  are  broken  at  intervals  to 
assist  the  appearance  of  gradually  fading  away.     Blue  ink  may  be  used  with  good  effect,  but 
should  be  employed  only  on  drawings  that  are  not  to  be  blueprinted  or  photographed  for  repro- 
duction. 

10.  Wood.     The  same  conventions  are  used  for  wood  in  section  as  were  described  in  the 
last  article,  and  shown  in  Plate  VI  for  wood  in  elevation. 

130.  Geological  Profiles  and  Sections.  The  nature  and  depths  of  soil  and  earth  are  deter- 
mined by  means  of  test  pits,  "  wash  borings,"  or  by  steel  sounding  rods,  while  diamond  drills 
are  used  for  exploring  rocky  substrata.  If  such  information  be  obtained  at  points  rather  close 
together  and  along  suitable  lines,  geological  profiles  or  sections  of  a  fair  degree  of  accuracy 
may  be  constructed. 

Plate  I£  shows  two  such  sections.  In  the  upper  one  are  shown  the  outlines  of  the  structure 
which  is  to  be  erected  along  the  line  where  the  section  is  taken.  Note  the  different  spacing 
of  the  lines  denoting  clay.  "  Soft  blue  clay  "  is  .properly  shown  by  lines  spaced  wide  apart  as 


WEST   LOCK  WALL 


^^&?    *ffi?"?&^ 


^Z///^  '/2^—^-t  vvyy^ 


Plate  IX. 

129 


Plate  X. 

131 


BOEINGS 


133 


compared  with  those  showing  "  stiff  blue  clay,"  while  those  in  the  stratum  marked  "  clay,  sand, 
and  gravel,  hard,"  are  still  farther  apart  to  allow  room  for  the  symbols  for  sand  and  gravel. 
The  alternation  of  direction  of  lines  in  the  several  strata 
also  helps  to  make  plain  their  lines  of  separation. 

In  the  lower  section  the  heavy  vertical  lines  and  the 
numbers  at  their  upper  ends  show  the  positions,  depths,  and 
numbers  of  the  borings  from  which  the  section  was  built  up. 

131.  Borings.     It  is  not  always  easy  to  build  up  a  geo- 
logical section  from  borings.     Rather  than  attempt  to  show 
complete  strata  from   evidence  which  may  be   capable  of 
more  than  one  interpretation,  it  is  customary  to  show,  espe- 
cially on  contract  drawings,  the  indications  furnished  by 
the  borings,  allowing  those  who  are  interested  in  the  matter 
to  interpret  for  themselves.     Fig.  55  exhibits  the  method 
of    showing    borings    on    profiles.      The    center    of    each 
boring  is  at  the  proper  station,  but  the  diameter  is  much 

exaggerated   so    as  to  make   room  for  the  symbols  ;    the  §»" 

vertical  depths  of  the  strata  and  of  the  whole  boring  are  to  the  vertical  scale  of  the  profile. 

132.  Illustration  of  Cross-Sectioning  and  Rendering.     Plate  X  shows  a  section  of  an  aque- 
duct at  a  culvert  which  passes  beneath.     It  illustrates  the  use  of  several  of  the  conventions 
described   above,  in  bringing  out  the   different  materials  and  showing  their  relations  in  the 
structure. 


CHAPTER  VIII 

COPYING,    REDUCTION,    AND   ENLARGEMENT   OF  PLANS 

133.  Copying  by  Blueprinting.  The  most  common  method  of  merely  duplicating  engi- 
neering drawings  is  by  the  process  of  blueprinting.  The  universal  adoption  of  this  method 
has  caused  a  complete  change  in  the  manner  in  which  nearly  all  sorts  of  plans  are  made. 
Whereas  they  were  formerly  made  on  thick  paper,  and  frequently  with  the  free  use  of  colors, 
both  in  inks  and  in  washes,  they  are  now  more  simply  made  on  thin,  translucent  tracing  paper 
or  cloth,  the  lines  being  generally  in  black  only.  The  use  of  colored  washes  to  express  differ- 
ent materials  in  section  has  given  place  to  the  use  of  conventional  combinations  of  lines,  as 
described  in  the  last  chapter.  All  these  changes  are  to  secure  drawings  which  may  be  blue- 
printed easily. 

For  making  blueprints  several  articles  are  necessary :  the  frame,  which  is  substantially 
like  any  photographic  printing  frame,  having  a  clear  glass  front  (plate  glass  if  the  frame  is 
more  than  two  feet  long),  and  a  removable  back  which  is  preferably  in  sections  hinged  to- 
gether; a  soft,  thick  pad  of  felt  or  woven  stuff  to  introduce  between  the  back  and  glass;  a 
tray  or  shallow  tank  for  washing  the  prints ;  and  the  sensitized  blueprint  paper. 

The  tracing  to  be  reproduced  is  first  placed  in  the  frame  with  its  face  against  the  glass. 
A  piece  of  the  sensitized  paper  somewhat  larger  than  the  tracing  is  then  placed  with  its  pre- 
pared face  against  the  back  of  the  tracing,  the  pad  is  placed  over  both,  and  the  back  is  secured 

134 


THE   SENSITIZING   SOLUTION  135 

in  place  by  means  of  wooden  bars  which  carry  springs  bearing  with  some  force  against  the 
back,  so  that  the  paper  and  the  tracing  are  held  in  close  contact.  The  whole  is  then  exposed  to 
the  sun,  which,  shining  through  the  glass  and  the  tracing,  produces  chemical  changes  in  the 
coating  of  the  paper  so  that  it  becomes  an  insoluble  Prussian  blue,  which  appears  as  such,  and 
is  fixed  against  further  change  by  washing  the  print  in  clean  water.  But  the  opaque  lines  of 
the  drawing  on  the  tracing  prevent  the  chemical  rays  of  the  sunlight  from  reaching  the  paper 
immediately  beneath  them,  so  that  when  the  print  is  immersed  in  water,  the  coating  of  the  paper 
at  these  pointjs  is  washed  away,  leaving  the  original  white  of  the  paper.  Thus  the  ordinary 
blueprint  shows  lines,  letters,  and  figures,  the  color  of  the  original  paper  on  a  blue  background. 
The  print  will  be  more  permanent  if  allowed  to  remain  in  the  bath  for  15  or  20  minutes  before 
being  hung  up  to  dry. 

The  time  of  exposure  to  the  sun  varies  greatly  with  different  papers.  Some  will  print  in 
30  seconds  in  bright  sunlight.  It  is  often  a  great  convenience  to  use  so  "  quick  "  a  paper,  but 
the  prints  are  likely  not  to  be  as  permanent  as  those  made  from  paper  requiring  an  exposure 
of  at  least  one  minute. 

There  is  a  great  difference  also  in  the  amount  of  overexposure,  or  "  burning,"  which 
different  papers  will  stand,  and  still  yield  fairly  good  prints.  In  all  cases  a  burned  print  must 
be  soaked  for  a  long  time  (say  an  hour)  to  bring  out  the  best  result. 

134.  The  Sensitizing  Solution  consists  essentially  of  red  prussiate  of  potash  and  ammo- 
nium ferric  citrate,  one  part  of  each  in  25  or  30  parts  of  water.  This  must  be  kept  away  from 
sunlight,  and  is  applied  with  a  sponge  in  a  dark  or  dimly  lighted  room.  A  thin  coating  is 
sufficient,  but  it  must  be  evenly  applied.  The  best  paper  has  a  smooth  hard  surface.  The 


136  COPYING,   KEDUCTION,  AND  ENLAKGEMENT 

prepared  paper  is  sold  so  cheaply  by  dealers,  and  in  such  variety  of  weight  and  texture,  that  it 
is  seldom  desirable  for  the  draftsman  to  prepare  it  for  himself. 

135.  Making  Corrections  on  Blueprints.     Lines  which  are  to  be  eliminated  may  be  gone 
over  carefully    with  water  color  mixed  to  match  the  color  of   the  background.     A  quicker 
method  is  to  apply  an  eraser  to  the  lines  until  the  blue  background  in  the  immediate  vicinity 
has  been  so  nearly  rubbed  off  that  the  lines  are  much  dimmed.     The  area  is  then  gone  over 
with  a  blue  pencil  and  a  stump  till  the  intensity  of  color  of  the  background  is  matched. 

Lines  may  be  added  to  a  print  with  Chinese  white,  but  a  better  result  is  obtained  by  the 
use  of  a  strong  solution  of  sodium  carbonate,  which  will  bleach  the  blue  of  the  background, 
thus  allowing  the  natural  color  of  the  paper  to  show  through.  The  solution  should  be  used 
in  a  new  writing  pen;  and  if  used  with  a  right-line  pen,  the  work  should  be  done  quickly,  and 
the  pen  should  be  thoroughly  cleaned  at  once,  as  the  solution  has  a  corrosive  action. 

If  additions  are  intended  to  be  prominent,  red  or  yellow  ink  or  water  color  may  be  added 
to  the  sodium  solution.  The  blue  will  still  be  bleached,  allowing  the  color  to  stand  upon  a 
white  background,  and  so  be  much  more  brilliant  than  if  applied  as  color  only  to  the  print. 
If,  however,  scarlet  vermilion  or  Dutch  chrome  be  mixed  very  thick  and  applied  to  the  print, 
the  effect  is  good. 

136.  The    Printing    Value    of     Colors.     If  colors,    either   in   the   form   of  pencils,  inks, 
or  water  colors,  are  used  on  a  tracing,  it  is  usually  of  some    importance  to  consider  what 
effect    these    will  have    upon  prints  ;  for  the  kind    of  color  as    well    as    its  density  is    a 
factor  in  its  printing  quality.     Broadly  speaking,  red  and    yellow  print    well,  while    blue 
does  not.    Green  prints  fairly  well  if  the  yellow  in  it  is  in  excess  of  the  blue,  as  does  also 


VANDYKE   NEGATIVES  137 

purple  if  the  red  is  in  preponderance.  Orange,  which  is  a  combination  of  red  and  yellow, 
prints  very  well.  Scarlet  vermilion,  if  mixed  thick,  prints  as  well  as  black.  Blue  is  often  used 
on  tracings  to  bring  out  water  surfaces,  but  it  must  be  put  on  very  heavily  if  its  effect  is  to  be 
secured  in  prints. 

137.  Printing   from  a  Thick  Drawing.     Prints  may  be  made   from   drawings   made   on 
Whatman's  or  other  opaque  drawing  paper,  and  even  on  Bristol  board,  by  first  saturating  the 
drawing  with  benzine  applied  with  a  cloth.     This  renders  the  paper  translucent  for  the  time 
being,  but  does  not  expand  it,  and  does  not  affect  the  ink. 

138.  Copying  by  Means  of  Vandyke  Negatives.     Vandyke  paper,  like  blueprint  paper,  is 
sensitized  for  printing  from  a  tracing  by  sunlight  or  by  electric  arc  light.     The  resulting 
prints  show  white  lines  on  a  Vandyke-brown  background.     These  prints  are  not  easy  to  read, 
but  if  such  a  one  be  used  for  printing  instead  of  the  original  tracing,  brown  lines  on  a  white 
ground  will  be  secured  if  Vandyke  paper  is  used,  or  blue  lines  on  a  white  ground  will  result  if 
ordinary  blueprint  paper  is  used.     The  first  print,  showing  white  on  brown,  is  called  a  nega- 
tive, for  in  making  it  the  tracing  is  placed  in  the  frame  with  its  back  to  the  glass,  thus  caus- 
ing  everything  on  the  resulting   print   to   read   backward,  as  in   a  photographic  negative. 
When  the  negative  is  used  instead  of  the  tracing  for  making  prints,  it  is  placed  in  its  turn 
with  its  back  to  the  glass,  and  the  final  prints  are  thus  made  to  read  direct.     The  object  of 
these  reversals  of  the  usual  order  is  to  avoid  bringing  the  thickness,  first  of  the  tracing,  and 
secondly  of  the  negative,  between  the  lines  of  the  drawing  and  the  sensitized  face  of  the  paper; 
otherwise  the  light  would  be  slightly  diffused  before  doing  its  work,  and  the  printed  lines 
would  not  be  so  clean-cut. 


138  COPYING,   REDUCTION,   AND  ENLARGEMENT 

The  process  of  printing  with  Vandyke  paper  is  exactly  like  that  with  blueprint  paper 
except  that  in  addition  to  the  water  bath  the  Vandyke  paper  is  given  a  bath  of  "  Vandyke  salt " 
solution,  which  intensifies  the  brown  color. 

139.  Making  Corrections  on  Vandyke  Negatives.     The  white  lines  may  be  stopped  out 
on  a  negative  by  the  use  of  any  opaque  water  color  or  with  India  ink.     An  "  erasing  fluid  " 
is  sold  by  dealers  which  bleaches  the  brown  color,  and  which  may  therefore  be  used  to  add 
white  lines  in  the  negative,  or  to  strengthen  dim  lines. 

140.  Special  Uses  of  Vandyke  Negatives.     The  Vandyke  process  affords  an  opportunity, 
as  does  no  other  process,  for  combining  parts  of  different  drawings  in  one  print,  and  of  chang- 
ing titles,  notes,  etc.,  on  prints.     Suppose,  for  instance,  that  the  title  of  a  drawing  is  to  be 
changed.     A  negative  of  the  drawing  is  made,  and  also  one  of  the  proposed  new  title.     The 
old  title  is  then  cut  from  the  negative  of  the  drawing,  the  piece  cut  out  being  slightly  smaller 
than  the  negative  of  the  new  title,  which  is  then  pasted  over  the  opening,  and  the  whole  is 
ready  for  use.     The  only  unusual  condition  is  that  there  are  two  thicknesses  of  paper  where 
the  pasting  is  done  ;  but  if  the  negatives  are  dense,  this  fact  will  not  be  shown  by  the  prints, 
and  at  the  worst  there  will  be  only  a  band  of  slightly  different  color  from  the  rest  of  the  back- 
ground. 

In  some  cases  original  plans  of  land  must  be  permanently  given  up,  as  when  they  are 
filed  in  county  registries  with  deeds  or  similar  instruments.  These  plans  are  usually  tracings, 
copies  of  which  it  is  desirable  to  keep.  Vandyke  negatives  may  be  made  from  such  tracings 
before  they  are  filed,  and  from  them  prints  may  be  made  as  needed. 


COPYING  139 

141.  Use  of  the  Copying  Glass.     When  a  copy  of  a  drawing  is  to  be  made  on  paper  so 
opaque  that  the  lines  of  the  original  cannot  be  seen  through  it,  the  copying  glass  (Art.  13)  is  a 
great  convenience.     The  drawing  is  first  laid  upon  the  glass,  and  over  this  is  placed  the  paper 
for  the  copy,  the  two  being  held  in  place  by  paper  weights,  or  by  thumb  tacks  if  their  edges 
extend  beyond  the  glass.     The  lights  from  the  lamps  below  will  render  the  lines  of  the  draw- 
ing plainly  visible,  and  they  may  be  simply  traced  upon  the  upper  sheet. 

142.  Copying  by  Pricking.     When  no  copying  glass  is  at  hand,  the  best  means  for  repro- 
ducing a  drawing  on  thick  paper  is  by  the  method  of  pricking.     The  blank  sheet  is  placed 
beneath  the  drawing  to  be  copied,  and  the  two  are  held  together  by  weights  or  thumb  tacks. 
A  pricker  (Art.  15)  is  then  thrust  through  the  salient  points  of  the  drawing  into  the  sheet 
beneath.     These  points  are  the  vertices  of  prominent  angles,  the  centers  of  circular  arcs,  and 
points  near  each  other  on  irregular  lines.     When  all  the  necessary  points  are  thus  transferred, 
a  few  of  the  most  important  ones  are  identified  on  the  lower  sheet  (a  corner  or  side  of  the 
upper  drawing  being  turned  back  to  give  access  to  the  lower  sheet),  and  joined  by  pencil 
lines.     A  few  such  lines  will  serve  to  identify  points  after  the  upper  sheet  is  entirely  removed, 
and  by  joining  them  with  pencil  lines  in  proper  order  the  whole  drawing  is  rapidly  built  up. 
If  the  drawing  is  quite  simple,  the  points  may  be  joined  at  once  by  ink  lines. 

143.  Copying  with  Transfer  Paper.     If  a  drawing  is  on  thin  paper,  it  may  be  copied  by 
means  of  transfer  paper.     The  ordinary  carbon  paper  used  by  typewriters  may  be  employed 
for  this  purpose,  or  a  substitute  may  be  made  as  described  in  Art.  17. 

The  drawing  to  be  copied  is  laid  face  up  upon  the  blank  sheet,  with  the  transfer  paper 
between  them,  its  prepared  face  being  turned  downward  upon  the  blank  sheet.     A  sharp  but 


140  COPYING,  REDUCTION,   AND  ENLARGEMENT 

smooth  point  (a  hard  pencil  will  do)  is  then  passed  with  a  little  pressure  over  the  lines  of  the 
drawing.  The  pressure  will  cause  the  sheet  below  to  be  blackened  along  the  path  of  the 
moving  point,  or  as  is  usually  stated,  the  lines  of  the  drawing  are  transferred  to  the  under 
sheet. 

144.  Copying,  Enlarging,  and  Reducing  by  the  Pantograph.     The  pantograph  was  described 
in  Art.  12.     This  instrument  is  not  frequently  found  in  engineers'  offices  because  a  really  good 
one  is  expensive,  and  because  it  takes  up  considerable  room.     It  is  of  great  advantage  in  re- 
ducing and  enlarging  drawings  because  it  works  rapidly,  reproduces  directly  (although  in 
pencil),  and,  when  the  arms  are  properly  set,  allows  no  chance  for  errors  except  such  as  arise 
from  a  poorly  made  instrument.     Moreover,  the  original  drawing  and  the  reduced  or  enlarged 
copy  may  be  on  any  kind  of  paper. 

145.  Reducing  and  Enlarging  by  Proportional  Squares.     By  this  method  the  drawing  to 
be  copied  is  first  ruled  into  squares,  as  shown  at  («),  Fig.  56.     For  convenience  the  squares 
are  lettered  from  left  to  right,  and  numbered  from  bottom  to  top.     The  rectangle  which  will 
contain  the  enlargement  or  reduction  in  the  desired  size  is  then  drawn  on  a  separate  sheet,  the 
ratio  of  width  to  length  being  the  same  as  that  of  the  width  to  length  of  the  original.     The 
rectangle  is  then  divided  into  the  same  number  of  squares  as  are  contained  in  the  original,  and 
the  squares  are  lettered  and  numbered  to  correspond  with  the  original,  as  shown  at  (5)  in  the 
figure. 

If  the  sides  of  the  squares  are  not  of  great  length,  and  if  extreme  accuracy  is  not  required, 
the  salient  points  of  the  drawing  may  be  located  merely  by  inspection.     For  instance,  point 


REDUCING  AND  ENLARGING 


G  in  (a),  Fig.  56,  is  seen  to  be  at  about  one 
third  of  the  distance  down  from  the  top  of 
square  D  -  4  and  about  one  fourth  of  the 
distance  from  left  to  right.  With  these 
relative  distances  in  mind  the  point  G  can 
be  located  with  considerable  accuracy  in 
the  corresponding  position  in  square  D-4 
of  (6). 

If  greater  accuracy  is  necessary,  pro- 
portional dividers  (Art.  6)  may  be  used  for 
locating  the  points  from  the  sides  of  the 
squares.  Some  parts  of  a  drawing  may 
contain  much  more  detail  than  others.  In 
this  case  the  squares  covering  the  position 
of  such  details  may  be  subdivided,  and  the 
work  followed  out  as  above  described. 

Curved  lines  are  generally  best  lo- 
cated by  noting  the  points  where  they 
cross  the  sides  of  squares.  If,  however,  the 
curve  is  a  circular  arc  whose  center  is  in 
the  drawing,  the  center  is  first  carefully 
located  and  the  curve  is  drawn  with  com- 
passes set  to  the  proper  radius. 





'  (a) 

Fig.  56. 


142 

There  may  be  objection  to  pencil  lines  even,  on  the  drawing  to  be  copied.  In  this  case 
the  squares  may  be  defined  on  tracing  cloth,  which  is  then  placed  upon  the  drawing,  thus  in 
effect  dividing  the  latter  into  squares.  The  cloth  is  sufficiently  transparent  so  that  the  lines  of 
the  drawing  show  through,  and  the  work  of  enlargement  or  reduction  progresses  as  above 
described. 

146.  Photography,  Lithography,  and  Photo-engraving.  Drawings  maybe  readily  copied  by 
photography.  The  copies  are  printed  directly  from  the  glass  negatives,  either  the  ordinary 
photographic  papers  or  ordinary  blueprint  paper  being  used.  Ordinarily  the  drawings  are 
considerably  reduced  when  reproduced  by  this  method,  and  with  a  good  lens  the  reduction  can 
be  made  quite  accurately  to  a  required  scale.  Large  negatives  are  expensive,  and  also  awkward 
and  bulky  to  preserve. 

Lithography  affords  a  most  satisfactory  means  of  reproducing  drawings  either  to  the  same 
or  to  a  reduced  scale.  The  process  is  costly  if  only  a  few  copies  are  required,  but  is  not  ex- 
pensive if  many  are  needed.  This  process  is  especially  adapted  to  the  production  of  large 
maps,  as  the  stones  from  which  they  are  printed  are  obtainable  in  large  sizes. 

Photo-engraved  Plates  usually  furnish  the  readiest  means  of  reproducing  maps  and  draw- 
ings if  the  number  desired  is  considerable,  if  the  greatest  dimension  is  not  more  than  two  feet, 
and  if  the  work  is  not  to  be  shown  in  colors. 

In  all  the  above-mentioned  processes  photography  plays  a  part  ;  in  photo-lithography  the 
lines  are  transferred  from  the  drawing  to  the  stone  by  means  of  one  or  more  photographic 
negatives,  while  in  photo-engraving  the  drawing  is  transferred  to  a  zinc  plate  by  photography, 
the  plate  then  being  etched  in  a  chemical  bath.  It  follows  that  the  original  drawing  must  be 


COLOR  WOEK  143 

made  only  in  such  colors  as  will  photograph  well.  The  same  colors  that  may  be  used  on  tracings 
for  blueprinting  (Art.  136)  may  be  used  in  drawings  which  are  to  be  photographed,  though  in 
general  there  is  no  reason  for  using  anything  but  perfectly  black  ink  for  this  purpose.  The 
lines  should  be  firm,  smooth,  and  not  too  fine. 

It  is  also  important  that  the  surface  on  which  the  drawing  is  made  shall  be  of  a  color 
which  will  not  act  upon  the  photographic  plate.  A  bluish- white  color  is  safest,  as  a  pure 
white  surface  is  likely  to  turn  yellow  with  age.  Tracing  cloth  presents  a  smooth,  even  surface 
of  a  bluish-white  color  ;  it  permits  changes  and  corrections  in  the  drawing,  and  is  therefore 
an  excellent  material  upon  which  to  draw  for  reproduction  by  any  photographic  process. 

Drawings  to  be  reduced  by  photo-engraving  are  usually  made  from  one  and  one  half  to 
three  times  the  size  desired  for  the  finished  work,  in  order  that  the  irregularities  in  the  lines 
may  be  eliminated  to  an  extent  by  the  reduction.  But  these  irregularities  are  only  reduced  — 
not  destroyed  —  by  the  reduction.  The  best  assurance  of  a  good  engraving  is  a  good  drawing. 

It  is  desirable  that  there  be  considerable  contrast  between  the  lightest  and  the  heaviest 
lines  of  a  drawing  for  photo-engraving,  for  in  the  prints  from  the  plates  the  light  lines  will  ap- 
pear slightly  heavier  (as  compared  with  the  heavy  lines)  than  they  are  in  the  original  drawing. 

When  a  drawing  is  to  be  reduced  by  any  one  of  the  processes  named  above,  its  graphical 
scale  should  be  shown,  so  that,  whatever  the  ratio  of  reduction,  a  record  of  the  scale  will  be 
preserved.  A  very  simple  form  of  graphical  scale  is  shown  in  Fig.  50. 

147.  Color  Work  by  Photo -engraved  Plates.  It  is  sometimes  desirable  to  show  in  color 
certain  lines  of  a  drawing,  as  for  instance  the  shore  and  the  water  lines  (Art.  57)  of  streams  and 
other  bodies  of  water.  In  this  case  as  many  drawings  are  made  as  there  are  colors  to  be  shown, 


144  COPYING,   REDUCTION,   AND  ENLARGEMENT 

each  drawing  containing  only  those  lines  which  are  to  be  printed  in  the  same  color.  A  plate 
is  then  made  from  each  drawing,  and  each  plate,  charged  with  ink  of  the  proper  color,  is  used 
in  the  press  in  turn,  contributing  its  particular  color  to  the  prints.  Thus  each  finished  print 
must  have  passed  through  the  press  as  many  times  as  there  are  colors  to  be  shown,  —  black 
being  counted  as  a  color  in  this  and  in  lithographic  work. 

The  printing  must  be  very  carefully  done  so  that  the  lines  of  each  plate  will  "register"; 
that  is,  be  printed  in  their  proper  positions  with  relation  to  the  lines  of  the  other  plates. 

The  original  drawings  are  all  made  in  black,  since  they  are  simply  to  be  photographed  for 
making  the  plates. 


ADVERTISEMENTS 


A  TEXT-BOOK  OF 

FREE-HAND  LETTERING 

By  FRANK  T.  DANIELS,  A.M.B. 

Author  of  "  A   Text- Book  of  Topographical  Drawing" 

WHEREVER  technical  drawing  is  taught  there  is  need  of  a  text-book  setting  forth 
the  elementary  principles  of  the  formation  of  letters,  of  their  combination  in 
words,  and  of  the  arrangement  of  words  in  titles.  This  book  is  published  to  supply 
this  need. 

Furthermore,  such  lettering  as.  a  draftsman  is  called  upon  to  do  must  be  done,  not 
only  well,  but  rapidly.  To  secure  either  speed  or  correct  proportion  the  student  must 
be  trained  to  do  good  lining,  free-hand^  and  to  estimate  accurately  both  distance  and 
direction.  The  exercises  in  this  book  are  designed  to  secure  such  results. 

The  practical  use  of  this  system  with  classes  has  shown  that  it  leads  to  rapidity  as 
well  as  excellence  of  execution. 

Cloth.     34.   Pages  of  Text.      ij   Folding  Plates.      Price,   75  cents 

D.   C.   HEATH   &   CO.,   Publishers 

BOSTON  NEW  YORK  CHICAGO 


ELEMENTS    OF 

MECHANICAL  DRAWING 

Use  of  Instruments,   Geometrical  Problems  and  Projection 
By  GARDNER  C.  ANTHONY,  A.M. 

Professor  of  Drawing  in    Tufts   College,   Dean  of  the  Bromfield- Pearson  School,   and  Member  of  the 

American    Society  of  Mechanical  Engineers 

THIS  is  a  text-book  rather  than  a  copy-book.  It  establishes  principles  and  suggests 
methods,  but  permits  freedom  in  their  application. 

The  system  of  projection  taught  is  that  which  the  best  practice  demands,  and  exam- 
ples have  been  selected  with  a  view  to  establishing  its  principles  with  the  least  expendi- 
ture of  time.  The  solution  of  geometric  problems  is  required  by  practical  methods  in  use 
by  draftsmen,  as  well  as  by  the  ordinary  geometric  construction. 

The  methods  employed  for  the  representation  of  objects  oblique  to  the  planes  of 
projection  give  a  clear  and  comprehensive  understanding  of  the  subject. 

The  graphic  statement  of  problems  enables  the  student  to  begin  drawing  without 
delay. 

Revised    Edition.      Cloth.      Illustrated.      1 60  pages.      $1.50 


D.   C.   HEATH   &   CO.,   Publishers 

BOSTON  NEW  YORK  CHICAGO 


MACHINE  DRAWING 

The  Principles  of  Machine  Drawing,  Sketching,  Figuring,  etc.,  with  Numerous 

Practical  Examples 

By  GARDNER  C.  ANTHONY,  A.M. 

Professor  of  Drawing  in   Tufts   College,   Dean  of  the  Bromfeld- Pear  son  School,  and  Member  of  the 

American   Society  of  Mechanical  Engineers 

THIS  treatise  teaches  the  application  of  the  principles  of  projection  to  the  illustration 
of  machinery,  and  the  more  concise  method  of  graphically  expressing  mechanical 
ideas.    It  also  informs  the  student  concerning  the  many  exceptions  to  the  laws  of  projec- 
tion, and  furnishes  practical  examples  to  serve  as  problems  to  students  and  suggestions 
to  draughtsmen. 

The  book  presupposes  a  knowledge  of  the  use  of  instruments  and  of  the  theory  of 
orthographic  projection.  It  is  the  advocate  of  no  special  system  of  lining,  figuring,  or 
lettering,  and  the  plates  represent  a  variety  of  types  in  drawing  which  will  be  serviceable 
to  the  draftsman  who  seeks  a  terse,  accurate,  and  complete  expression  of  mechanical 
ideas. 

Cloth.      65   Pages  of  Text.      18   Folding  Plates  with  4.0   Illustrations.      Price,  $1.50 


D.   C.   HEATH   &   CO.,   Publishers 

BOSTON  NEW  YORK  CHICAGO 


ESSENTIALS  OF  GEARING 

By  GARDNER  C.  ANTHONY,  A.M. 

Professor   of  Drawing  in    Tufts    College,   Dean  of  the  Bromfeld- Pearson   School,   and  Member  of  the 

American  Society  of  Mechanical  Engineers 

THIS  treatise  comprises  the  course  of  instruction  and  problems  given  by  Professor 
Anthony  in  college  and  evening  drawing  schools  for  several  years  past,  and  is  the 
result  of  his  practical  experience  in  connection  with  designing  and  constructing  gears. 

Besides  numerous  cuts  there  are  fifteen  folding  plates  illustrating  the  principles  and 
practice  of  describing  gear  teeth.  A  series  of  progressive  problems  is  given,  illustrating 
the  principles  set  forth  in  the  text,  and  also  designed  to  encourage  thorough  investigation 
of  the  subjects  by  suggesting  lines  of  thought  and  study  beyond  the  limits  of  this  book. 

A  definite  lay-out  for  each  problem  is  given,  the  necessary  instruction  for  its  solution 
is  clearly  stated,  and  numerous  references  to  the  text  require,  the  student  to  make  a  care- 
ful study  of  the  subject  before  performing  the  problem.  This  enables  a  variety  of  original 
problems  to  be  solved  by  a  class  with  no  additional  labor  on  the  part  of  the  instructor. 


Cloth.      84.  pages  of  Text  and  15  Folding  Plates.      Price,  $I.$O 


D.   C.   HEATH   &  CO.,   Publishers 

BOSTON  NEW  YORK  CHICAGO 


AN  INITIAL  PINE  OF  25  CENTS 

WILL  BE  ASSESSED  FOR  FAILURE  TO  RETURN 
HIS  BOOK  ON  THE  DATE  DUE.  THE  PENALTY 
WILL  INCREASE  TO  SO  CENTS  ON  THE  FOURTH 
DAY  AND  TO  $I.OO  ON  THE  SEVENTH  DAY 
OVERDUE. 


^?-*s* 


MtK- 


*PJH34r 


-4W- 


APR  22  1947 


UNIVERSITY  OF  CALIFORNIA  LIBRARY 


